FUZRUF-onto: a Methodology to Develop Fuzzy Rough Ontologies

FUZRUF-onto: a Methodology to Develop Fuzzy Rough Ontologies | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Method Article FUZRUF-onto: a Methodology to Develop Fuzzy Rough Ontologies rawan sanyour This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3927799/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Nowadays, semantic web technologies play a crucial role in knowledge representation paradigm. With the raise of imprecise and vague knowledge, there is an upsurge demand in applying a concrete well-established procedure to represent such knowledge. Ontologies, particularly fuzzy ontologies are increasingly applied in application scenarios in which handling of vague knowledge is significant. However, such fuzzy ontologies utilize fuzzy set theory to provide quantitative methods to manage vagueness. In various cases of real-life scenarios, people need to express their everyday requirements using linguistic adverbs such as very, exactly, mostly, possibly, etc. The aim is to show how fuzzy properties can be complemented by Rough Set methods to capture another type of imprecision caused by approximation spaces. Rough sets theory offers a qualitative approach to model such vagueness via describing fuzzy properties at multiple levels of granularity using approximation sets. Using rough-set theory, each fuzzy concept is represented by two approximations. The lower approximation PL(C) consists of a set of fuzzy properties that are definitely observable in the concept. The upper approximation PU(C) on the other hand contains fuzzy properties that are possibly associated with the concept but may not be observed. This paper introduces a methodology named FUZRUF-onto methodology, which is a formal guidance on how to build fuzzy rough ontologies from scratch using extensive research in the area of fuzzy rough combination. Fuzzy set and rough set theories are applied to capture the inherently fuzzy relationships among concepts expressed by natural languages. The methodology provides a very good guideline for formally constructing fuzzy rough ontologies in terms of completeness, correctness, consistency, understandability, and conciseness. To explain how the FUZRUF-onto works, and demonstrate its usefulness, a practical step by step example is provided. Fuzzy sets Fuzzy theory Rough sets Fuzzy ontologies Ontology engineering Knowledge representation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1. Introduction Ontologies provide an explicit representation of a generalized conceptualization. It has been proven to be one of the most effective modeling technique to represent knowledge [ 1 ] [ 2 ]. They have been used in various areas including semantic web, soft computing, artificial intelligence, software engineering, and natural language processing [ 3 ]. According to [ 4 ] ontologies can be defined as an explicit formal specification that represent real world concepts and relationships in a specific domain promoting the establishment of interrelationships with other models in an automatic manner. Despite the undisputed success of ontologies, classical ontologies have been deemed as inadequate for semantically representing vague and imprecise knowledge reflected in various real world domains [ 5 ]. The vagueness phenomenon represented by everyday terms and concepts such as close, hot, tall, very, roughly, etc. are quite common in human languages and cannot be precisely extended in certain domains and concepts. This is because, often, such concepts have fuzzy boundaries that don’t have a sharp distinction between entities that fall within and those which are don’t. Representing such vagueness in an ontology-based form is important not only because it is presented in several domains but also because, in several application scenarios, considering such vagueness and impreciseness can significantly enhance system’s effectiveness [ 6 ] [ 7 ]. Fuzzy sets theory, rough sets theory and fuzzy logic [ 8 ][ 9 ][ 10 ][ 11 ] have been proved to be suitable formalisms to manage vague and imprecise knowledge in real world domains. Fuzzy rough ontologies compromise a new knowledge representation paradigm that can be effectively utilized in application scenarios in which vague or imprecise knowledge is rising in importance. In the next section, a comprehensive novel methodology, called FUZRUF-onto methodology, is proposed for developing reusable and sharable fuzzy rough ontologies from the scratch. It can significantly enhance the effectiveness of fuzzy rough ontology development process, and improve its quality in terms of accuracy, shareability and reusability of the resulted ontology. The proposed methodology provides a concrete guideline to i) precisely identify vague knowledge within a specific domain, ii) model this knowledge by means of fuzzy rough ontology elements in an explicit and accurate way. It is worth noting that although the methodological aspects of the fuzzy ontologies development process has been so far neglected except in FODM [ 12 ] and IKARUS-Onto [ 13 ], however, they don’t introduce the rough set theory in which linguistic hedges (also called modifiers) can be considered as special linguistic expressions to describe the vague properties of fuzzy concepts. Generally, linguistic hedges (modifiers) are special linguistic expressions by which linguistic terms are modified. They can be classified into two categories, i.e., the intensive hedges such as very, and the weakened hedges such as more or less. Some hedges move one term to another, while some intensify or weaken the degree of a term. The FUZRUF-onto is the first methodology that combined fuzzy set and rough set theories to precisely identify the uncertainty in context dependent characteristics of objects, thus, express users preferences more accurately through raising the confidence level of the inferred context. The reminder of this paper is organized as follows: theoretical preliminaries are presented in section two, section three shows the proposed FUZRUF-onto with detailed specifications for each phase, a practical example of constructing a fuzzy rough ontology following the proposed methodology is presented in section four. Finally, a discussion conclusion is introduced in section five. 2. Preliminaries a) Fuzzy Logic and fuzzy sets Fuzzy logic and fuzzy set theory were firstly introduced by Zadeh [ 14 ] to handle imprecise and vague knowledge. In contrast of the classical set theory in which elements either belong to a specific set or not, in fuzzy sets, element can be a set member with some degree. For example, if X is a set of elements, a fuzzy subset A of X can be defined by a membership function µ A (X) that assign any x \(\in\) X to a value in the interval of real numbers between 0 and 1. An element has a 0 value means that no membership while element with 1 value represents a full membership. This change in the classical true/false convention has led to a new type of propositions called fuzzy propositions. Each of these propositions can have a degree of truthiness belong to [0,1]. Such degree reflects the compatibility of a fuzzy proposition with a given state of facts. For instance, the truth of a proposition saying that a given person is tall is clearly a matter of degree. All crisp set operations such as intersection, union, complement and implication set are extended to fuzzy sets using t-norm function, a t-conorm function, a negation function and an implication function respectively. For a formal definition of these functions, we refer the reader to [ 15 ][ 16 ]. b) Rough and fuzzy rough sets Fuzzy set theory provides a quantitative way to represent vagueness in knowledge using degrees of membership to fuzzy concepts. On the contrary, rough set theory offers a qualitative approach to manage this vagueness. Instead of using a degree of membership, rough sets are used to approximate vague concepts. It is an effective way when it is not possible to quantify the membership function of these vague concepts. Rough sets were firstly introduced by Pawlak in 1982 [ 17 ]. The key idea is to approximate the vague concept when there is no complete information about that concept. when there are only few elements belong to the concept, and there is an indiscernibility equivalence relation, i.e., reflexive, symmetric, and transitive relation between elements, a vague concept can be approximated by means of two concepts: Lower approximation and upper approximation. The lower approximation defined by the sets of elements that are definitely belong to the vague set. These elements may not be complete and not include some of the elements and features and contains all the indistinguishable elements of the vague set. On the other hand, the upper approximation describes the set of elements that possibly belong to the vague set, i.e., elements that might not actually belong to the vague concept. This set may consist of some elements that are indistinguishable from the vague set. A rough set then can be defined as a pair of these two approximations: lower and upper approximations. Fuzzy logic and rough logic together can be considered as complementary formalisms to address impreciseness and vagueness in knowledge representation. An extension of the rough sets named fuzzy rough sets [ 9 ][ 11 ][ 18 ] can be considered through defining a fuzzy similarity relation instead of the indiscernibility equivalence relation between elements. While in rough sets an element can only belong to one equivalent class of similar elements, in fuzzy rough sets, an element can belong to several fuzzy similarity classes with different degrees of truth. There are some other fuzzy sets approximations such as tight approximation in which all the existing fuzzy similarity classes are included, and loose approximation that considers the best one among the similarity classes. 3. FUZRUF-onto methodology as mentioned earlier, the FUZRUF-onto is a methodology that defines a set of well-defined steps and guidelines to represent vouge knowledge by means of fuzzy set and rough set theories. It aims to help both ontology engineers and domain experts to effectively model the vagueness of the domain as accurately as possible. The methodology assumes prior knowledge of ontology development from those who use it. The lifecycle of FUZRUF-onto is depicted in Fig. 1 . At each phase, the list of actions that required to be performed and people involved (i.e., ontology engineer and/or domain expert) are defined. The entire six phases and their associated activities are elaborated in the following subsections. a) Phase1: ontology purpose and scope the first task in the proposed methodology is to identify the motivation behind building the fuzzy rough ontology. This is determined by identifying to what extent both vagueness and roughness are presented in the context domain. This step is essential since that it defines the purpose of using such ontologies and estimates the required work to develop the ontology. In order to ideally establishing the purpose and the scope, several questions are required to be explicitly answered: i) in which domain and what is the scope of the knowledge that required to be modeled using thin ontology, ii) based on the determined field and scope, what is the type of the represented ontology, is it domain-specific?, application-specific or a generic ontology?, iii) who will be involved in the process of ontology development and what role each of the participants is going to play. In this step, both ontology engineers and domain experts are involved and cooperate to capture the vagueness and its requirements within the targeted domain. Once these questions are answered accurately, the role of domain expert is to identify the specialized knowledge by which the requirement of fuzziness is determined. This could be accomplished by providing a deep information about the domain and the application scenario of the ontology to be developed. After that, the ontology engineer starts to ensure that the captured vagueness is required by the selected domain and check whether it is well represented in the application scenario. Fuzziness might exist in different ontology elements whose meaning could be interpreted as “vague” in the specified domain/scenario. These elements could be: Vague concepts : an ontology concept is said to be vague if there is an indetermination in the initiating of its individuals. This type of concepts often indicates phases or qualitative states (e.g. big, medium, adult, old, young. etc.). Vague relations and attributes : an ontology relation is considered to be vague if, in the given scenario, application or domain, there is a pair of individuals for which there is an indetermination in its inclusion into such relation. Vague attribute value terms : often, these attributes are gradable attributes which their potential values can be represented using vague terms. Attributes such as tall, large, short, etc. could be considered as primary candidates for expressing such terms. During this phase, it is essential to ensure that the identified vagueness is sufficient as a base to establish the necessity of developing the fuzzy rough ontology. b) Phase2: identifying the ontology elements. The second phase in the methodology is a comprehensive identification of both vague and crisp knowledge by which ontology elements are explicitly described. The goal of this step is to ensure that the defined elements have a precise and clear meaning, thus, can be reusable in other similar works. The identification of these elements could be categorized into two fundamental steps: i) defining the crisp ontology elements, ii) defining the fuzzy ontology elements. Defining crisp ontology elements: in the proposed methodology, any element in the domain knowledge that is not involved in the fuzzy related information can be considered as a crisp element. In the literature, there are several works such as [ 19 ] that provide crisp ontologies development methodologies and techniques. At this stage, elements such as classes, properties, concepts, and relationships are enumerated and organized in a hierarchal manner. Defining these elements falls out of the scope of this paper. Defining fuzzy ontology elements: Several researchers defined the fuzzy ontology as the ontology in which its elements including concepts, attributes and relations are fuzzified [ 20 ]. However, fuzzy ontologies O F represent the domain knowledge in terms of both crisp and fuzzy elements [ 21 ]. The main goal of this step is to provide a well-defined approximation of the vague and uncertain information through fuzzy degrees in the defined domain. Here, the role of the domain expert is essential to identify a clear and precise specification based on their experience and historical data. The fuzzy ontology elements that model vague information are defined by the ontology engineer in a well-organized manner. The procedure of defining these elements is quite similar to that followed in crisp ontology development methodologies. However, the difference is that how precisely captures the vagueness and represent it using fuzzy sets. The first element to identify is the fuzzy concept. Often, in several cases, fuzzy concepts acquire their vagueness from some fuzzy attached relations, attributes and terms. In this case, the defined concept’s vagueness and the interpretation of its instances fuzzy degrees can be derived from those attached elements such as in [ 22 ] [ 23 ]. Otherwise, fuzzy concepts can be defined as the same way as in the case of defining fuzzy relations and attributes (through assigning fuzzy degrees to instances pairs) [ 24 ]. Definition 3.1. A fuzzy concept C f is a concept in which its instances belong to it at certain degrees. This degree indicates that at which extent this instance could be considered as an instance of this concept. For example, the concept “young person” represents the people that are classified to be young. This type of fuzzy concepts has at least one fuzzy property P f . Each fuzzy concept has a set of elements: C f ={N cf , P, P f } Where: N cf is the name of the fuzzy concept. For example, “TallPerson”, “OldPerson”, “BaldPerson”. P is the set of non-fuzzy (crisp) properties. P f is the set of fuzzy properties. Definition 3.2. The second element to identify is the fuzzy property P f . Fuzzy properties are properties that assign a specific value to each concept instance at a certain degree. Such degree indicates that to what extent the assigned value is applicable to an instance for the given attribute. The fuzzy property is a property represented with a fuzzy linguistic variable [ 21 ]. P f = {N pf , T, MF} Where: N pf is the name of the fuzzy property. e.g., age, height, price, income, etc. T is a set of terms that represent the values of the property. E.g., T = height = {short, middle-height, tall}. MF is a membership function that map each term in T to a fuzzy set. Figure 2 depicts an example of a fuzzy concept with its fuzzy property. After defining the set of fuzzy attributes, whose values could be expressed by a set of vague terms, fuzzy datatypes could be identified. Fuzzy datatypes (fuzzy linguistic variables) are sets of vague terms that can be used within the fuzzy ontology as property values. For instance, as shown in Fig. 3 , the property “age” compromise terms such as young, middle-aged, and old. The role of fuzzy datatype here is to map each of these terms to a fuzzy set by which its meaning is defined through assigning a fuzzy degree to each term’s potential exact value. For example, an age of 30 is considered young at a degree of .5 and considered middle-aged at the same degree. Note that the different value ranges of the fuzzy set are often defined by the domain expert and differ upon different domains. For example, the age 30 is considered young at a degree of .5 in a specific domain while considered young at a degree of 1 in another. Definition 3.3. The third element to define is the fuzzy relations. A Fuzzy relation R f is a semantic relation that relates concepts instances at a certain degree. This degree indicates that to what extent this relation between the two instances should be considered true. It determines whether these two instances belong to the relation. As in the case of fuzzy properties, fuzzy relation in the fuzzy ontology can be represented by fuzzy linguistic variables. R f = {N rf , T, MF} Where: N rf is the name of the fuzzy relation. e.g., distance. T is a set of terms that represent the values of the relation. E.g., T = age= {short, middle, long}. MF is a membership function that map each term in T to a fuzzy set. As illustrated in figure 4, the fuzzy relation distance shows that to what extent the distance between the linked instances classifies as “near” to each other. At the end of this phase, the vagueness of the fuzzy elements and the interpretation of their fuzzy degrees would be explicitly defined. This step will provide not only a comprehensive understanding of the vague meaning of the fuzzy ontology but also allows domain experts to accurately assign the fuzzy degrees to the elements’ instances. c) Phase3: approximating the vague fuzzy concepts and sets using linguistic modifiers, i.e., hedges, through fuzzy rough sets (approximators). linguistic hedges (also called modifiers) can be considered as special expressions by which the degree of membership of fuzzy datatype could be modified. These hedges will be utilized to describe the vague properties of fuzzy concepts. Using these modifiers, fuzzy context dependent characteristics of objects could be adequately identified, thus, express users’ preferences more accurately through adjusting the confidence level of the inferred context [ 25 ]. Often, in natural language, humans often use adjectives and adverbs in order to describe what they want. “Adjectives” are used to express fuzzy properties while hedges and modifiers (adverbs) could be used to impose emphasizes on these properties by mapping the fuzzy set into a modified fuzzy set. If the meaning of a linguistic adjective is denoted by a fuzzy set A \(\in\) F(X) , then the meaning of the term modified by a linguistic modifier (an adverb), is denoted by m(A) where m is a linguistic modifier representing the adverb in question. Definition 1 Given a nonempty fuzzy domain X, a fuzzy modifier m on X is a F(X) → F(X) mapping. In the literature, there are several modifiers such as very, extremely, definitely, more or less, roughly, almost, possible, etc. which are used with adjectives (terms) that represented by fuzzy sets as follows: : = extremely | roughly | very | exactly | almost | possible | rather | etc. : = | More or less and roughly are called weakening modifiers, very and extremely are intensifying adverbs and at least and at most are ordering based modifiers [ 26 ]. The role of these modifiers is to alter the fuzzy value (membership value) of a property, thus, enrich the ontologies semantics and increase users satisfaction [ 27 ]. This could be achieved by identifying the lower, i.e., sub-concept, and upper, i.e., super-concept approximation of the fuzzy set by which the fuzzy target set can be represented by two other fuzzy sets; one identifies the features that definitely describe the fuzzy target set, and the other identifies the features that possibly describe the fuzzy target set. For any given universe X , an equivalence (fuzzy) relation R and a fuzzy set F in X , by using an implicator \(\Rightarrow\) and a t-norm \(\otimes\) , the pair lower and upper approximations (R∗(F); R* (F)) are called fuzzy rough sets in ( X, R ) such that for every x ∈ X , R∗(F)(x) = inf max {1 − R(x; y); F(y)} (1) y∈X R*(F)(x) = sup min {R(x; y); F(y)} (2) y∈X where inf is the greatest lower bound, and sup is the least upper bound of the set. Various linguistic hedges can be modeled by means of these upper and lower approximations as shown in table1 [ 3 ][ 9 ][ 25 ][ 28 ]. Approximations such as tight lower, loose, lower, tight upper, and loose upper could be constructed through approximating the lower and the upper fuzzy rough sets. For the mathematical background of using fuzzy rough approaches to represent linguistic hedges, readers are referred to [ 29 ][ 30 ][ 31 ]. Table 1 Examples of Linguistic Modifiers with their Corresponding Fuzzy Rough approximations and Membership d) Phase 4: reusing existing ontology’s elements. At this phase, several existing ontologies are checked to determine its relevance to the domain and scope of interest, thus its reusability. This could effectively reduce the workload of designing new ontologies form scratch and allow for interoperability and compatibility with other applications in same/different domains. Both crisp and fuzzy ontology elements with similar specifications, impreciseness and vagueness modeling could be utilized in the new proposed ontology. However, these elements, especially fuzzy elements may not be fit to be used as they are in the new ontology. As a result, domain experts should be involved to correct and refine them into the identified specifications in the domain of interest to match the new ontology requirements. For instance, the fuzzy datatype “YoungAge” is defined in an existing ontology with the range of 20–40. In some cases, this definition of young people may need to be refined by domain experts to fit the new requirements. At the end of this phase, inherited vague information such as “people aged from 20 to 40 could be regarded as young people” and accurately approximated to represent the intended domain and application. e) Phase 5: formalization of the constructed ontology The goal of this step is to transform the designed fuzzy rough ontology into a well-established machine-readable format through fuzzy ontology languages. The classical ontology languages may not be suitable to represent the vagueness and imprecision that defined in the fuzzy ontologies [ 8 ]. Therefore, several languages have been developed to support them. The role of ontology engineer here is to consider the characteristics of each available language and their reasoning capabilities to adequately reason the presented vague knowledge. For example, fuzzy datatypes are supported by some (not all) fuzzy ontology languages such as fuzzy OWL2 annotations [ 3 ] while supporting fuzzy datatypes themselves differ by means of fuzzy concrete domains [ 32 ] or fuzzy linguistic variables such as in [ 33 ][ 34 ]. f) Phase 6: validation of fuzzy ontology The success of creating an ontology is subject to the validation result. The designed fuzzy rough ontology should go through the following check list to ensure it has represented the intended model of the world. The usefulness of the developed ontology can be subjectively validated to ensure that: The fuzzy rough ontology is correct: particularly, all the fuzzy elements reflect a meaning that is indeed vague in the identified domain. This could be achieved by another team of the domain experts to verify that all definitions are correct. The fuzzy rough ontology is accurate: namely, the identified degree of the fuzzy rough elements is accurately and intuitively approximating the targeted vagueness. This could be done by another domain experts team to guarantee that the degrees are intuitively correct. The fuzzy rough ontology is complete: the ontology has met all the identified requirements. Particularly, all the information that has vague meanings has been precisely captured and represented. This could be achieved by a team of domain expert through checking that the non-fuzzy parts (i.e., crisp parts) don’t convey any vouge meaning. The fuzzy rough ontology is consistent: namely, there are no elements containing controversial definitions about the domain’s vagueness in the developed ontology. Fuzzy reasoners can be used to check the developed ontology consistency. The fuzzy rough is understandable: ensure that all the defined terms are self-explanatory, and the constructed ontology can be easily understood by domain experts, ontology engineers and the intended users who have been involved in the development process. 4. Practical example: a use case of developing a generic fuzzy rough context ontology a) Phase 1: motivation (establishing the need for fuzzy rough ontology) Today, users want to use their handheld devices to access data and request services upon their context related information such as location, time and environment. Context information can effectively enhance the applications usability through allowing them to adopt to their surrounding changing environment. They use linguistic adverbs and adjectives to describe what they need. For example, they can be interested in finding “the closest restaurant to their workplace”. But, to what extent we can consider a specific place as “close”, and how to deal with this type of requests. Fuzzy and rough theories allow to tackle this issue through reasoning with non-crisp ontology concepts. This vagueness and impreciseness can be handled by defining appropriate linguistic variables and modifiers through which truth degrees are identified depending on a specific level of certainty. According to the context awareness targeted domain, the intended modeled information is focused on the 5Ws questions (who, when, what, where and why). Who is the user? What is he doing? When it was happened? where is the location? And why this would be happened? The relationships in the developed ontology should represent the user context: an environment has a location and devices which provide some services, a user who uses his/her device to request such services at this location that has a specific activity carried out in a specific moment. However, for these relationships, it is required to establish linguistic specifications with threshold values (often defined by the domain expert) to extract the concepts instances that satisfies the selected values. For instance, according to user requirements, the relation “distance in” that relates the user concept to the location concept can be expressed using three different linguistic variables: located in, close to, far from. A close place to some users is not close for another, thus, the borderline between these terms is vague and overlap between them could be exist. Therefore, the definition for these linguistic terms should be fuzzified to meet the domain requirements. Moreover, b) Phase 2: defining the ontology’s elements. Here, domain experts and ontology engineers collaboratively work to provide a precise distinction between fuzzy related information and crisp information. As a result, the knowledgebase will be partitioned into two different parts: precise information (crisp elements) and fuzzy rough related information. The crisp elements will be identified to acquire the precise information by which the targeted domain will be modeled. For the needs of this demonstration and given the publication’s length and clarity considerations, we limit the ontology to the following elements. We distinguish among six main entities: User, Location, PersonalStatus, Environment, Activity, and Action. All these elements together define the 5Ws questions related to user’s context: Who, What, When, Where, and Why. Figure 5 shows the initial layout of the constructed ontology with the identified concepts and sub concepts. User: this class represents a single unique user who has some properties such as profile, calendar, and mobility situation. It is responsible for representing the user as an observed entity in the environment. A specific user represents a specific role according to the targeted domain. For instance, a user can be a tourist, patient, visitor, lecturer, shopper, etc. Environment: this class represents an organized hierarchy of indoor and outdoor locations, and their generic and specific features. For example, in the office environment, offices, meeting rooms, lecture rooms, conference rooms, kitchen, toilets, etc., are examples of locations in an environment. An environment can have some associated weather measurements such as Humidity, Temperature, Lighting, and Pressure. Action: actions can be seen as an atomic event performed by the user with a timestamp, e.g., EnterBuilding, OpenDoor, WalkBy, TurnOnLight, etc. Activity: activity can be considered as a single or composite set of actions with an “inherent intend” with a StartDateTime and EndDateTime. For example, AttendinMeeting, DoingPresentation, MakingCoffee, ScheduledEvent, VisitingLocation, etc. An activity is a set of weighted, compulsory and/or optional actions. Some activities could be divided into more specific sub smaller activities such as Lecturing activity that can be either GiveLecture or AttendLecture. Location: this class can be any indoor or outdoor location in which a specific user is located in, nearby, or far from. Indoor locations can be a public building such as a hospital, shopping mall, restaurant, department, etc. or a private building such as a home, a room (lecture room, meeting room, conference room), etc. Outdoor locations include a metro, park, street, train, terrace, etc. PersonalStatus: the personal status of a user represents his status at a specific moment. Status can be Available, OnLeave, Away, Busy, etc. Figure 6 depicts the different six concepts with their specifications represented in Protégé. Fuzzy Datatypes and Fuzzy Concrete Roles (data properties) typical data properties in the original ontology can be transformed into fuzzy datatypes with ranges expressed using data range expressions such as (double 0.0] and double [ < = 1000.0]) for hasDistance data property range. Fuzzy concrete roles are defined in FuzzyOWL2 by setting its range datatype to one of the predefined fuzzy datatypes. An annotation example in OWL2 for the defined datatype CloseToDistance is as follows Listing 1: Annotation for a New Fuzzy Datatype CloseToDistance Using Trapezoidal Modifier The fuzzy datatypes defined in the user’s context fuzzy rough ontology are: StillMobility, MovingMobility : these two fuzzy datatypes used to represent user’s situation, i.e., whether he is moving with a specific speed (km/h) or he is still in his place. The concrete role User. hasMobility indicates his situation in that particular time. LocatedInDistance, CloseToDistance, FarFromDistance : are used to approximate the distance of the user from a specific place (in meters). The concrete role User. hasDistance indicates the distance in meters between the user and a specific location. DryHumidity, NormalHumidity, HumidHumidity : are used to model humidity (in percentage). The concrete role Location. hasHumidity indicates the humidity level of a specific Location. ColdTemperature, WarmTemperature, HotTemperature : are used to measure temperature (in Celsius degrees). The concrete role Location. hasTemperature indicates the temperature of a specific Location. DarkLighting, DimLighting, NormalLighting, BrightLighing : are identified to measure lighting (in lumens). The concrete role Location. hasLighting indicates the amount of light getting out from a bulb in a specific Location within an environment. ShortDuration, MediumDuration, LongDuration : are used to represent duration (in minutes). The concrete role Activity. hasDuration indicates the duration of a specific activity. CloseToTime, FarFromTime : are used to approximate the duration of time (in minutes) between two different activities/actions. the concrete roles {Activity, Action}. CloseToTime indicates the duration of time between activities/actions. Figure 7 depicts the fuzzy datatypes and fuzzy concrete roles (data properties) identified using Protégé (partial). Note that, the figure shows both the identified data properties including fuzzy and non-fuzzy ones. Fuzzy Abstract Roles (Fuzzy Object Properties). By assigning a fuzzy membership value, the object properties in the original ontology can be converted to fuzzy abstract roles. Some of these roles in the developed ontology are: User- IsLocatedIn -Location: Represents the location of a user in a given moment. A fuzzy degree can approximate the degree of which a specific user is located in a specific location. User- Attend -Event: Identifies a given user who attends an event. An even can be an appointment in the user’s calendar. User- Perform -Activity: Specifies which user performs an Activity. Given a fuzzy degree here, represents the level of uncertainty about whether the user performs the specified activity. User- PerformAction -Action: Specifies which User performs an Action. Given a fuzzy degree here, represents the level of uncertainty about whether the user performs the specified action. User- HasStatus -PersonalStatus: Indicates a personal status of any user in certain moment. For example, a user can be available, on-leave, away, and busy. User- ParticipateIn -Activity: Specifies a given user who participate in a specific activity. A fuzzy degree can approximate the degree of which a specific user is participating in a specific activity. Activity- HappenIn -Location Represents the location of an activity in a given moment. A fuzzy degree can approximate the degree of which a specific activity is located in a specific location. Action- ActionHappenIn -Location Represents the location of an action in a given moment. A fuzzy degree can approximate the degree of which a specific action is located in a specific location. Figure 8 shows some of the identified fuzzy/crisp object properties in Protégé. It is worth noting that in the previously identified elements, there are no explicit vague concepts, and the vagueness (the lack of precise boundaries between vague attributes) is occurred because of some relations and attributes. c) Phase 3: approximating the vague fuzzy concepts/sets using linguistic modifiers/hedges through fuzzy rough sets (approximators). Linguistic modifiers (also referred to as linguistic hedges) are specific type of linguistic expressions like very, extremely, more or less, quiet. While applied to adjectives, linguistic hedges allow us to express an emphasis we impose on the corresponding properties. They can be considered as special expressions by which the degree of membership of fuzzy datatype/relation could be modified. hedges such as very, extremely, definitely, more or less, roughly, almost, possible, etc., are utilized to describe the vague properties of fuzzy concepts. These modifiers are modeled by means of the construction of upper and lower approximations of the identified fuzzy concepts and relations. For example, given the fuzzy datatype property CloseToDistance between (User, Location), the fuzzy modifier Very is identified to modify the value of the membership function of that datatype and hence, the newly identified VeryCloseToDistance datatype makes the user not only Close to a specific location, but VeryClose to that location. Listing 2 expresses this modification in OWL2. Listing 2: Datatype “CloseToDistance” modified by “very” modifier. Linguistic fuzzy rough sets (also called fuzzy necessity and fuzzy possibility) will be used to tune the membership function values according to users’ preferences and requirements. This could be achieved through using (1) and (2). For example, the term “close” in the fuzzy relation IsLocatedIn can be expressed by the formula 𝑅(𝑥, 𝑦) = max (0, min (1, 3.5 - \(\frac{\left|x-y\right|}{100}\) )) And fuzzy membership function: $${\mu }\left(\text{c}\text{l}\text{o}\text{s}\text{e}\right)= \left\{\begin{array}{c}\frac{x-0}{500-0} 0\le x\le 500\\ 1 500<x\le 1000\\ \frac{1500-x}{1500-1000} 10001500, x<0\end{array}\right.$$ As shown from the previous function, a place that distant 600M is close to the user with 1 confidence value (the value of the \({\mu }\) ). However, if the user decided to discover the places that are “very” close, this value will be tuned to be .8 for the same distance using the lower approximation. The lower approximation of the fuzzy term “close” can be calculated to find the new membership value for the same place when it required to be considered as “very close”. Figure 9 illustrates the membership function values for the “close” and “VeryClose” distances. The second fuzzy element is the attribute “temperature”. The fuzzy term “Warm” that represents one of the weather conditions can be expressed using 𝑅(𝑥, 𝑦) = min (1, max (0, 2 - \(\frac{\left|x-y\right|}{2}\) )) and the following membership function: $${\mu }\left(\text{W}\text{a}\text{r}\text{m}\right)= \left\{\begin{array}{c} \frac{x-0}{19-0} 0\le x\le 19\\ 1 19<x\le 24\\ \frac{28-x}{28-24} 2428, x<0\end{array}\right.$$ As seen from the function, the temperature degree 14 is considered warm with .7 confidence degree. However, the same temp. degree is considered “very warm” with just .6 confidence value. It is worth noting that the linguistic modifier “very” again used to tune this value using the lower approximation of the fuzzy term “warm”. Figure 10 depicts the difference between the confidence values of the term “Warm” and “very Warm” temperature. Another fuzzy attribute in the constructed ontology is the “user mobility” by which the mobility of a specific user, throughout estimating his/her speed, is evaluated. The following membership function illustrates the confidence values of the user mobility according to the detected speed. $${\mu }\left(\text{S}\text{t}\text{i}\text{l}\text{l}\right)= \left\{\begin{array}{c} 1 x<2\\ \frac{5-\text{x}}{3} 25\end{array}\right.$$ For example, if the user is moving with 3 km/h speed, we can say that he is still with .7 confidence value. However, in some cases, we need to discover the “possibility” that this user is “still”. In such case, the upper approximation of this fuzzy set needs to be calculated using the upper approximation formula (table1). Figure 11 depicts how values of the membership function of different speeds were changed when the “possibility” of user movement is considered. For instance, the truth value is increased from .5 to .8 when checking whether a user with 3.5 km/h speed is “possibly” still rather than “just” still. The last two fuzzy relations are IsScheduledAt/ IsOccurredAt. As previously explained, these two relations express the time approximation of a specific event/action to be started/occurred. The following is the membership function that can be used to calculate the confidence value of the difference (in minutes) between two specific event, activity or action. $${\mu }\left(\text{C}\text{l}\text{o}\text{s}\text{e}\right)= \left\{\begin{array}{c} 1 x<30\\ \frac{50-x}{20} 3050\end{array}\right.$$ As shown, the 43 minutes difference between two activities makes them close with .4 confidence level. On the other hand, this value is increased up to .6 when to check whether these two activities are “possibly” close to each other (using the upper approximation). Figure 12 shows the difference between these membership values considering “close” and “possibly close” fuzzy terms. d) Phase 4: reusing existing ontology elements in the constructed ontology, as illustrated in the concepts taxonomy, there are some general concepts such as time and location that can be reused from the publically available ontologies instead of rebuilding them from the scratch. [ 36 ] [ 37 ]. e) Phase 5: formalization of the constructed ontology In this use case, OWL2 could be selected as the formalism language to represent the designed ontology model. Ontology editors such as the fuzzy-OWL protégé extension could be utilized in this phase. Protégé provides an easy user-friendly tool to visually implement the designed ontologies and allows for automatic generation of the code in different languages such as OWL and RDF. For example, Syntax and semantics of RDF are extended to support real numbers of the interval [0,1] to be expressed as degrees subjects, objects, and predicates [ 38 ]. In addition, there are a set of fuzzy extensions of description logics as in [ 39 ] that could be utilized to enable this transformation process. Bobillo et al. [ 40 ], and Nilavu and Sivakumar [ 3 ] introduced a concrete methodology to formalize fuzzy and fuzzy rough ontologies using OWL2 annotation properties. It is worth noting that different ontology formalism languages vary from each other in terms of characteristics, rules, and capabilities they have. There is no a standard mechanism to evaluate these languages regarding their strength and weakness in representing a specific ontology element. Therefore, the formalism language should be chosen according to constructed ontology’s requirements. f) Phase 6: validation of the constructed ontology The validation results serve as proof of the usefulness of the developed fuzzy rough ontology. Although the consistency of the constructed ontology could be evaluated by the fuzzyDL reasoner, the other features should be subjectively examined by the ontology engineers, domain experts, and ontology users who have been involved in the development process. Specifically, the validation results are presented in the following: The developed fuzzy rough ontology is correct. The vagueness that is reflected in all identified fuzzy elements is precisely captured and implemented with correctly identified fuzzy rough sets. In addition, the links between the crisp and fuzzy elements have been accurately identified. In order to verify the constructed ontology, another domain expert could be consulted. The developed ontology is consistence. Even though the consistency characteristic is often evaluated by the fuzzy description logic reasoner, both structure and content don’t have any controversial definitions regarding the domain vagueness in the developed ontology. The developed ontology is complete. All the constructed elements have precisely captured the vagueness meaning identified in the different phases and covered all the knowledge requirements. Here, additional domain experts could be consulted to ensure that the identified crisp parts do not contain any vague meaning. The developed ontology is understandable. Since that all the defined terms are self-explanatory, the constructed ontology can be easily understood by domain experts, ontology engineers and the intended users. The developed ontology is conciseness. All the identified elements are accurately approximating the degree of vagueness in an intuitive way. 5. Discussion and conclusion The proposed methodology can be considered as a set of activities by which a fuzzy rough ontology is built in a logic order. The essential goal of this methodology is to provide a methodological guideline to follow in order to construct this type of ontologies, thus ensuring an enhanced performance comparing to intuitive ontology constructing works. As stated in the introduction, The FUZRUF-onto is the first methodology that combines fuzzy set and rough set theories to precisely identify context dependent characteristics of objects, thus, express users preferences more accurately through tuning the confidence level of the inferred context. As shown in the practical use case, the context ontology has been successfully constructed following the step-by-step guideline provided by the FUZRUF-onto phases. During the development process, each of these phases has been set with precise purposes and to do list. It is clear that using the FUZRUF-onto, both efficiency and accuracy can be enhanced in fuzzy rough ontologies development process. For theoretical methodology, it is quite difficult to perform a quantitative and comparison analysis with existing methodologies. Reviewing the relevant literature, it has been noticed that there is a lack of a well-established quantitative analysis and evaluation to compare and test new developed methodologies with other existing ontology methodologies [ 13 ]. For example, METHONTOLOGY [ 41 ], the well-known crisp ontology methodology does not include any sort of evaluation. Likewise, although they proved their applicability by providing some experimental scenarios and use cases, some other works such as NeON [ 42 ], Diligent [ 43 ] and [ 44 ] have not provided any rigorous evaluation. Due to the subjective nature of this field, current research community just accepts the way an ontology development methodology is introduced even with the exclusion of the evaluation part. Similarly, as the developed methodology was accompanied with a detailed description of the vague knowledge and an explicit interpretation of each phase, it is expected to provide an effective enhancement in the fuzzy rough ontology development process due to the following reasons: Comparing with the existing non-methodological ontology development processes in which ontology engineers build the ontology based on their preferences and intuition, the developed methodology provides them a well-established development process. The only overhead that could be introduced in this type of methodologies is the time required to understand, learn, and practice the methodology phases. The proposed methodology focuses on the knowledge representation (including both crips and fuzzy knowledge) at the conceptual level rather than the actual technical representation. This allows developers to focus on the development process without worrying about the formalization process. As stated earlier, the detailed description of the vague knowledge and the explicit interpretation of the fuzzy degrees, and their approximations using rough sets ensures that everybody involved in the development process, including domain experts and ontology engineer, can define the vagueness meaning in an easier, more complete and more accurate manner. The detailed fuzzy rough ontology elements identification phases allow the constructed ontology to become sharable and reusable by other developers in different domains. As the developed methodology categorize the targeted domain knowledge into two different parts: crisp information and fuzzy information, ontology engineers can precisely identify the borderline between them, thus find different approaches to model them. For the crisp part, existing ontology development methodologies could be utilized which allows engineers to focus on the fuzzy part. The proposed methodology can be considered as the first of its type of methodological guideline for building fuzzy rough ontologies from the scratch. Starting from identifying the motivation, going through defining and approximating the fuzzy sets elements, reusing other external ontology elements and ending up validating the designed ontology. Following the methodology phases, developers can build a fuzzy rough ontology in which the fuzzy sets are approximated to tune the membership function values according to users’ preferences and requirements. 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G. da Costa, “Uncertainty modeling process for semantic technology,” PeerJ Comput. Sci. , vol. 2016, no. 8, pp. 1–36, 2016. Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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17:05:32","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1153320,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3927799/v1/8e24ffc3-4085-4dc7-b904-65b782266350.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eFUZRUF-onto: a Methodology to Develop Fuzzy Rough Ontologies\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eOntologies provide an explicit representation of a generalized conceptualization. It has been proven to be one of the most effective modeling technique to represent knowledge [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. They have been used in various areas including semantic web, soft computing, artificial intelligence, software engineering, and natural language processing [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. According to [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] ontologies can be defined as an explicit formal specification that represent real world concepts and relationships in a specific domain promoting the establishment of interrelationships with other models in an automatic manner.\u003c/p\u003e \u003cp\u003eDespite the undisputed success of ontologies, classical ontologies have been deemed as inadequate for semantically representing vague and imprecise knowledge reflected in various real world domains [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. The vagueness phenomenon represented by everyday terms and concepts such as close, hot, tall, very, roughly, etc. are quite common in human languages and cannot be precisely extended in certain domains and concepts. This is because, often, such concepts have fuzzy boundaries that don\u0026rsquo;t have a sharp distinction between entities that fall within and those which are don\u0026rsquo;t. Representing such vagueness in an ontology-based form is important not only because it is presented in several domains but also because, in several application scenarios, considering such vagueness and impreciseness can significantly enhance system\u0026rsquo;s effectiveness [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFuzzy sets theory, rough sets theory and fuzzy logic [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e][\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e][\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e][\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] have been proved to be suitable formalisms to manage vague and imprecise knowledge in real world domains. Fuzzy rough ontologies compromise a new knowledge representation paradigm that can be effectively utilized in application scenarios in which vague or imprecise knowledge is rising in importance.\u003c/p\u003e \u003cp\u003eIn the next section, a comprehensive novel methodology, called FUZRUF-onto methodology, is proposed for developing reusable and sharable fuzzy rough ontologies from the scratch. It can significantly enhance the effectiveness of fuzzy rough ontology development process, and improve its quality in terms of accuracy, shareability and reusability of the resulted ontology. The proposed methodology provides a concrete guideline to i) precisely identify vague knowledge within a specific domain, ii) model this knowledge by means of fuzzy rough ontology elements in an explicit and accurate way.\u003c/p\u003e \u003cp\u003eIt is worth noting that although the methodological aspects of the fuzzy ontologies development process has been so far neglected except in FODM [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] and IKARUS-Onto [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], however, they don\u0026rsquo;t introduce the rough set theory in which linguistic hedges (also called modifiers) can be considered as special linguistic expressions to describe the vague properties of fuzzy concepts. Generally, linguistic hedges (modifiers) are special linguistic expressions by which linguistic terms are modified. They can be classified into two categories, i.e., the intensive hedges such as very, and the weakened hedges such as more or less. Some hedges move one term to another, while some intensify or weaken the degree of a term. The FUZRUF-onto is the first methodology that combined fuzzy set and rough set theories to precisely identify the uncertainty in context dependent characteristics of objects, thus, express users preferences more accurately through raising the confidence level of the inferred context.\u003c/p\u003e \u003cp\u003eThe reminder of this paper is organized as follows: theoretical preliminaries are presented in section two, section three shows the proposed FUZRUF-onto with detailed specifications for each phase, a practical example of constructing a fuzzy rough ontology following the proposed methodology is presented in section four. Finally, a discussion conclusion is introduced in section five.\u003c/p\u003e"},{"header":"2. Preliminaries","content":"\u003cp\u003e\u003cstrong\u003ea) Fuzzy Logic and fuzzy sets\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFuzzy logic and fuzzy set theory were firstly introduced by Zadeh [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e] to handle imprecise and vague knowledge. In contrast of the classical set theory in which elements either belong to a specific set or not, in fuzzy sets, element can be a set member with some degree. For example, if X is a set of elements, a fuzzy subset A of X can be defined by a membership function \u0026micro;\u003csub\u003eA\u003c/sub\u003e\u003cem\u003e(X)\u003c/em\u003e that assign any \u003cem\u003ex\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\in\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003eX\u003c/em\u003e to a value in the interval of real numbers between 0 and 1. An element has a 0 value means that no membership while element with 1 value represents a full membership. This change in the classical true/false convention has led to a new type of propositions called fuzzy propositions. Each of these propositions can have a degree of truthiness belong to [0,1]. Such degree reflects the compatibility of a fuzzy proposition with a given state of facts. For instance, the truth of a proposition saying that a given person is tall is clearly a matter of degree. All crisp set operations such as intersection, union, complement and implication set are extended to fuzzy sets using t-norm function, a t-conorm function, a negation function and an implication function respectively. For a formal definition of these functions, we refer the reader to [\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e][\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eb) Rough and fuzzy rough sets\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFuzzy set theory provides a quantitative way to represent vagueness in knowledge using degrees of membership to fuzzy concepts. On the contrary, rough set theory offers a qualitative approach to manage this vagueness. Instead of using a degree of membership, rough sets are used to approximate vague concepts. It is an effective way when it is not possible to quantify the membership function of these vague concepts. Rough sets were firstly introduced by Pawlak in 1982 [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e]. The key idea is to approximate the vague concept when there is no complete information about that concept. when there are only few elements belong to the concept, and there is an indiscernibility equivalence relation, i.e., reflexive, symmetric, and transitive relation between elements, a vague concept can be approximated by means of two concepts: Lower approximation and upper approximation. The lower approximation defined by the sets of elements that are definitely belong to the vague set. These elements may not be complete and not include some of the elements and features and contains all the indistinguishable elements of the vague set. On the other hand, the upper approximation describes the set of elements that possibly belong to the vague set, i.e., elements that might not actually belong to the vague concept. This set may consist of some elements that are indistinguishable from the vague set. A rough set then can be defined as a pair of these two approximations: lower and upper approximations.\u003c/p\u003e\n\u003cp\u003eFuzzy logic and rough logic together can be considered as complementary formalisms to address impreciseness and vagueness in knowledge representation. An extension of the rough sets named fuzzy rough sets [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e][\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e][\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e] can be considered through defining a fuzzy similarity relation instead of the indiscernibility equivalence relation between elements. While in rough sets an element can only belong to one equivalent class of similar elements, in fuzzy rough sets, an element can belong to several fuzzy similarity classes with different degrees of truth. There are some other fuzzy sets approximations such as tight approximation in which all the existing fuzzy similarity classes are included, and loose approximation that considers the best one among the similarity classes.\u003c/p\u003e"},{"header":"3. FUZRUF-onto methodology","content":"\u003cp\u003eas mentioned earlier, the FUZRUF-onto is a methodology that defines a set of well-defined steps and guidelines to represent vouge knowledge by means of fuzzy set and rough set theories. It aims to help both ontology engineers and domain experts to effectively model the vagueness of the domain as accurately as possible. The methodology assumes prior knowledge of ontology development from those who use it. The lifecycle of FUZRUF-onto is depicted in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. At each phase, the list of actions that required to be performed and people involved (i.e., ontology engineer and/or domain expert) are defined. The entire six phases and their associated activities are elaborated in the following subsections.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea) Phase1: ontology purpose and scope\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ethe first task in the proposed methodology is to identify the motivation behind building the fuzzy rough ontology. This is determined by identifying to what extent both vagueness and roughness are presented in the context domain. This step is essential since that it defines the purpose of using such ontologies and estimates the required work to develop the ontology. In order to ideally establishing the purpose and the scope, several questions are required to be explicitly answered: i) in which domain and what is the scope of the knowledge that required to be modeled using thin ontology, ii) based on the determined field and scope, what is the type of the represented ontology, is it domain-specific?, application-specific or a generic ontology?, iii) who will be involved in the process of ontology development and what role each of the participants is going to play. In this step, both ontology engineers and domain experts are involved and cooperate to capture the vagueness and its requirements within the targeted domain.\u003c/p\u003e\n\u003cp\u003eOnce these questions are answered accurately, the role of domain expert is to identify the specialized knowledge by which the requirement of fuzziness is determined. This could be accomplished by providing a deep information about the domain and the application scenario of the ontology to be developed. After that, the ontology engineer starts to ensure that the captured vagueness is required by the selected domain and check whether it is well represented in the application scenario. Fuzziness might exist in different ontology elements whose meaning could be interpreted as \u0026ldquo;vague\u0026rdquo; in the specified domain/scenario. These elements could be:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eVague concepts\u003c/strong\u003e: an ontology concept is said to be vague if there is an indetermination in the initiating of its individuals. This type of concepts often indicates phases or qualitative states (e.g. big, medium, adult, old, young. etc.).\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eVague relations and attributes\u003c/strong\u003e: an ontology relation is considered to be vague if, in the given scenario, application or domain, there is a pair of individuals for which there is an indetermination in its inclusion into such relation.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eVague attribute value terms\u003c/strong\u003e: often, these attributes are gradable attributes which their potential values can be represented using vague terms. Attributes such as tall, large, short, etc. could be considered as primary candidates for expressing such terms.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eDuring this phase, it is essential to ensure that the identified vagueness is sufficient as a base to establish the necessity of developing the fuzzy rough ontology.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eb) Phase2: identifying the ontology elements.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe second phase in the methodology is a comprehensive identification of both vague and crisp knowledge by which ontology elements are explicitly described. The goal of this step is to ensure that the defined elements have a precise and clear meaning, thus, can be reusable in other similar works. The identification of these elements could be categorized into two fundamental steps: i) defining the crisp ontology elements, ii) defining the fuzzy ontology elements.\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eDefining crisp ontology elements: in the proposed methodology, any element in the domain knowledge that is not involved in the fuzzy related information can be considered as a crisp element. In the literature, there are several works such as [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e] that provide crisp ontologies development methodologies and techniques. At this stage, elements such as classes, properties, concepts, and relationships are enumerated and organized in a hierarchal manner. Defining these elements falls out of the scope of this paper.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eDefining fuzzy ontology elements: Several researchers defined the fuzzy ontology as the ontology in which its elements including concepts, attributes and relations are fuzzified [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. However, fuzzy ontologies O\u003csub\u003eF\u003c/sub\u003e represent the domain knowledge in terms of both crisp and fuzzy elements [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e]. The main goal of this step is to provide a well-defined approximation of the vague and uncertain information through fuzzy degrees in the defined domain. Here, the role of the domain expert is essential to identify a clear and precise specification based on their experience and historical data. The fuzzy ontology elements that model vague information are defined by the ontology engineer in a well-organized manner. The procedure of defining these elements is quite similar to that followed in crisp ontology development methodologies. However, the difference is that how precisely captures the vagueness and represent it using fuzzy sets.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe first element to identify is the \u003cstrong\u003efuzzy concept.\u003c/strong\u003e Often, in several cases, fuzzy concepts acquire their vagueness from some fuzzy attached relations, attributes and terms. In this case, the defined concept\u0026rsquo;s vagueness and the interpretation of its instances fuzzy degrees can be derived from those attached elements such as in [\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e] [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e]. Otherwise, fuzzy concepts can be defined as the same way as in the case of defining fuzzy relations and attributes (through assigning fuzzy degrees to instances pairs) [\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDefinition 3.1.\u0026nbsp;\u003c/strong\u003eA \u003cstrong\u003efuzzy concept\u003c/strong\u003e C\u003csub\u003ef\u003c/sub\u003e is a concept in which its instances belong to it at certain degrees. This degree indicates that at which extent this instance could be considered as an instance of this concept. For example, the concept \u0026ldquo;young person\u0026rdquo; represents the people that are classified to be young. This type of fuzzy concepts has at least one fuzzy property P\u003csub\u003ef\u003c/sub\u003e. Each fuzzy concept has a set of elements:\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u0026nbsp;\u003c/sub\u003e\u003cem\u003e={N\u003c/em\u003e\u003csub\u003e\u003cem\u003ecf\u003c/em\u003e,\u003c/sub\u003e \u003cem\u003eP, P\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e}\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eN\u003csub\u003ecf\u003c/sub\u003e is the name of the fuzzy concept. For example, \u0026ldquo;TallPerson\u0026rdquo;, \u0026ldquo;OldPerson\u0026rdquo;, \u0026ldquo;BaldPerson\u0026rdquo;.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eP is the set of non-fuzzy (crisp) properties.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eP\u003csub\u003ef\u003c/sub\u003e is the set of fuzzy properties.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDefinition 3.2.\u0026nbsp;\u003c/strong\u003eThe second element to identify is the \u003cstrong\u003efuzzy property\u003c/strong\u003e P\u003csub\u003ef\u003c/sub\u003e. Fuzzy properties are properties that assign a specific value to each concept instance at a certain degree. Such degree indicates that to what extent the assigned value is applicable to an instance for the given attribute. The fuzzy property is a property represented with a fuzzy linguistic variable [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e\u0026nbsp;\u003cem\u003e= {N\u003c/em\u003e\u003csub\u003e\u003cem\u003epf\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eT, MF}\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eN\u003csub\u003epf\u003c/sub\u003e is the name of the fuzzy property. e.g., age, height, price, income, etc.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eT is a set of terms that represent the values of the property. E.g., T\u0026thinsp;=\u0026thinsp;height = {short, middle-height, tall}.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eMF is a membership function that map each term in T to a fuzzy set. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e depicts an example of a fuzzy concept with its fuzzy property.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eAfter defining the set of fuzzy attributes, whose values could be expressed by a set of vague terms, fuzzy datatypes could be identified. \u003cstrong\u003eFuzzy datatypes\u003c/strong\u003e (fuzzy linguistic variables) are sets of vague terms that can be used within the fuzzy ontology as property values. For instance, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e, the property \u0026ldquo;age\u0026rdquo; compromise terms such as young, middle-aged, and old. The role of fuzzy datatype here is to map each of these terms to a fuzzy set by which its meaning is defined through assigning a fuzzy degree to each term\u0026rsquo;s potential exact value. For example, an age of 30 is considered young at a degree of .5 and considered middle-aged at the same degree. Note that the different value ranges of the fuzzy set are often defined by the domain expert and differ upon different domains. For example, the age 30 is considered young at a degree of .5 in a specific domain while considered young at a degree of 1 in another.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDefinition 3.3.\u0026nbsp;\u003c/strong\u003eThe third element to define is the fuzzy relations. A \u003cstrong\u003eFuzzy relation\u003c/strong\u003e R\u003csub\u003ef\u003c/sub\u003e is a semantic relation that relates concepts instances at a certain degree. This degree indicates that to what extent this relation between the two instances should be considered true. It determines whether these two instances belong to the relation. As in the case of fuzzy properties, fuzzy relation in the fuzzy ontology can be represented by fuzzy linguistic variables.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e\u0026nbsp;\u003cem\u003e= {N\u003c/em\u003e\u003csub\u003e\u003cem\u003erf\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eT, MF}\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eN\u003csub\u003erf\u003c/sub\u003e is the name of the fuzzy relation. e.g., distance.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eT is a set of terms that represent the values of the relation. E.g., T\u0026thinsp;=\u0026thinsp;age= {short, middle, long}.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eMF is a membership function that map each term in T to a fuzzy set.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eAs illustrated in figure 4, the fuzzy relation distance shows that to what extent the distance between the linked instances classifies as \u0026ldquo;near\u0026rdquo; to each other.\u003c/p\u003e\n\u003cp\u003eAt the end of this phase, the vagueness of the fuzzy elements and the interpretation of their fuzzy degrees would be explicitly defined. This step will provide not only a comprehensive understanding of the vague meaning of the fuzzy ontology but also allows domain experts to accurately assign the fuzzy degrees to the elements\u0026rsquo; instances.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ec) Phase3: approximating the vague fuzzy concepts and sets using linguistic modifiers, i.e., hedges, through fuzzy rough sets (approximators).\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003elinguistic hedges (also called modifiers) can be considered as special expressions by which the degree of membership of fuzzy datatype could be modified. These hedges will be utilized to describe the vague properties of fuzzy concepts. Using these modifiers, fuzzy context dependent characteristics of objects could be adequately identified, thus, express users\u0026rsquo; preferences more accurately through adjusting the confidence level of the inferred context [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e]. Often, in natural language, humans often use adjectives and adverbs in order to describe what they want. \u0026ldquo;Adjectives\u0026rdquo; are used to express fuzzy properties while hedges and modifiers (adverbs) could be used to impose emphasizes on these properties by mapping the fuzzy set into a modified fuzzy set. If the meaning of a linguistic adjective is denoted by a fuzzy set \u003cem\u003eA\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\in\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003eF(X)\u003c/em\u003e, then the meaning of the term modified by a linguistic modifier (an adverb), is denoted by \u003cem\u003em(A)\u003c/em\u003e where m is a linguistic modifier representing the adverb in question.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDefinition 1\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eGiven a nonempty fuzzy domain X, a fuzzy modifier m on X is a F(X) \u0026rarr; F(X) mapping.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eIn the literature, there are several modifiers such as very, extremely, definitely, more or less, roughly, almost, possible, etc. which are used with adjectives (terms) that represented by fuzzy sets as follows:\u003c/p\u003e\n\u003cp\u003e\u0026lt;modifier\u0026gt;: = extremely | roughly | very | exactly | almost | possible | rather | etc. \u0026lt;fuzzy term\u0026gt;: = \u0026lt;adjective\u0026gt; | \u0026lt;modifier\u0026thinsp;\u0026gt;\u0026thinsp;\u0026lt;\u0026thinsp;adjective\u0026gt;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eMore\u003c/em\u003e or \u003cem\u003eless\u003c/em\u003e and \u003cem\u003eroughly\u003c/em\u003e are called weakening modifiers, \u003cem\u003every\u003c/em\u003e and \u003cem\u003eextremely\u003c/em\u003e are intensifying adverbs and \u003cem\u003eat least\u003c/em\u003e and \u003cem\u003eat most\u003c/em\u003e are ordering based modifiers [\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e]. The role of these modifiers is to alter the fuzzy value (membership value) of a property, thus, enrich the ontologies semantics and increase users satisfaction [\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e]. This could be achieved by identifying the lower, i.e., sub-concept, and upper, i.e., super-concept approximation of the fuzzy set by which the fuzzy target set can be represented by two other fuzzy sets; one identifies the features that definitely describe the fuzzy target set, and the other identifies the features that possibly describe the fuzzy target set. For any given universe \u003cem\u003eX\u003c/em\u003e, an equivalence (fuzzy) relation \u003cem\u003eR\u003c/em\u003e and a fuzzy set \u003cem\u003eF\u003c/em\u003e in \u003cem\u003eX\u003c/em\u003e, by using an implicator \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Rightarrow\\)\u003c/span\u003e\u003c/span\u003e and a t-norm \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\otimes\\)\u003c/span\u003e\u003c/span\u003e, the pair lower and upper approximations \u003cem\u003e(R\u0026lowast;(F); R* (F))\u003c/em\u003e are called fuzzy rough sets in (\u003cem\u003eX, R\u003c/em\u003e) such that for every \u003cem\u003ex\u003c/em\u003e \u0026isin; \u003cem\u003eX\u003c/em\u003e,\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eR\u0026lowast;(F)(x)\u0026thinsp;=\u0026thinsp;inf max {1\u0026thinsp;\u0026minus;\u0026thinsp;R(x; y); F(y)} (1)\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003csub\u003e\u003cem\u003ey\u0026isin;X\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eR*(F)(x)\u0026thinsp;=\u0026thinsp;sup min {R(x; y); F(y)} (2)\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003csub\u003e\u0026nbsp;\u003cem\u003ey\u0026isin;X\u003c/em\u003e\u0026nbsp;\u003c/sub\u003e\u003c/p\u003e\n\u003cp\u003ewhere \u003cem\u003einf\u003c/em\u003e is the greatest lower bound, and \u003cem\u003esup\u003c/em\u003e is the least upper bound of the set. Various linguistic hedges can be modeled by means of these upper and lower approximations as shown in table1 [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e][\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e][\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e][\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e]. Approximations such as tight lower, loose, lower, tight upper, and loose upper could be constructed through approximating the lower and the upper fuzzy rough sets. For the mathematical background of using fuzzy rough approaches to represent linguistic hedges, readers are referred to [\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e][\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e][\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eTable 1 Examples of Linguistic Modifiers with their Corresponding Fuzzy Rough approximations and Membership\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" alt=\"\" width=\"867\" height=\"351\" /\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ed) Phase 4: reusing existing ontology\u0026rsquo;s elements.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAt this phase, several existing ontologies are checked to determine its relevance to the domain and scope of interest, thus its reusability. This could effectively reduce the workload of designing new ontologies form scratch and allow for interoperability and compatibility with other applications in same/different domains. Both crisp and fuzzy ontology elements with similar specifications, impreciseness and vagueness modeling could be utilized in the new proposed ontology.\u003c/p\u003e\n\u003cp\u003eHowever, these elements, especially fuzzy elements may not be fit to be used as they are in the new ontology. As a result, domain experts should be involved to correct and refine them into the identified specifications in the domain of interest to match the new ontology requirements. For instance, the fuzzy datatype \u0026ldquo;YoungAge\u0026rdquo; is defined in an existing ontology with the range of 20\u0026ndash;40. In some cases, this definition of young people may need to be refined by domain experts to fit the new requirements. At the end of this phase, inherited vague information such as \u0026ldquo;people aged from 20 to 40 could be regarded as young people\u0026rdquo; and accurately approximated to represent the intended domain and application.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ee) Phase 5: formalization of the constructed ontology\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe goal of this step is to transform the designed fuzzy rough ontology into a well-established machine-readable format through fuzzy ontology languages. The classical ontology languages may not be suitable to represent the vagueness and imprecision that defined in the fuzzy ontologies [\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e]. Therefore, several languages have been developed to support them. The role of ontology engineer here is to consider the characteristics of each available language and their reasoning capabilities to adequately reason the presented vague knowledge. For example, fuzzy datatypes are supported by some (not all) fuzzy ontology languages such as fuzzy OWL2 annotations [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e] while supporting fuzzy datatypes themselves differ by means of fuzzy concrete domains [\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e] or fuzzy linguistic variables such as in [\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e][\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ef) Phase 6: validation of fuzzy ontology\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe success of creating an ontology is subject to the validation result. The designed fuzzy rough ontology should go through the following check list to ensure it has represented the intended model of the world. The usefulness of the developed ontology can be subjectively validated to ensure that:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eThe fuzzy rough ontology is correct: particularly, all the fuzzy elements reflect a meaning that is indeed vague in the identified domain. This could be achieved by another team of the domain experts to verify that all definitions are correct.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe fuzzy rough ontology is accurate: namely, the identified degree of the fuzzy rough elements is accurately and intuitively approximating the targeted vagueness. This could be done by another domain experts team to guarantee that the degrees are intuitively correct.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe fuzzy rough ontology is complete: the ontology has met all the identified requirements. Particularly, all the information that has vague meanings has been precisely captured and represented. This could be achieved by a team of domain expert through checking that the non-fuzzy parts (i.e., crisp parts) don\u0026rsquo;t convey any vouge meaning.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe fuzzy rough ontology is consistent: namely, there are no elements containing controversial definitions about the domain\u0026rsquo;s vagueness in the developed ontology. Fuzzy reasoners can be used to check the developed ontology consistency.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe fuzzy rough is understandable: ensure that all the defined terms are self-explanatory, and the constructed ontology can be easily understood by domain experts, ontology engineers and the intended users who have been involved in the development process.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"4. Practical example: a use case of developing a generic fuzzy rough context ontology","content":"\u003cp\u003e\u003cstrong\u003ea) Phase 1: motivation (establishing the need for fuzzy rough ontology)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eToday, users want to use their handheld devices to access data and request services upon their context related information such as location, time and environment. Context information can effectively enhance the applications usability through allowing them to adopt to their surrounding changing environment. They use linguistic adverbs and adjectives to describe what they need. For example, they can be interested in finding \u0026ldquo;the closest restaurant to their workplace\u0026rdquo;. But, to what extent we can consider a specific place as \u0026ldquo;close\u0026rdquo;, and how to deal with this type of requests. Fuzzy and rough theories allow to tackle this issue through reasoning with non-crisp ontology concepts. This vagueness and impreciseness can be handled by defining appropriate linguistic variables and modifiers through which truth degrees are identified depending on a specific level of certainty.\u003c/p\u003e\n\u003cp\u003eAccording to the context awareness targeted domain, the intended modeled information is focused on the 5Ws questions (who, when, what, where and why). Who is the user? What is he doing? When it was happened? where is the location? And why this would be happened? The relationships in the developed ontology should represent the user context: an environment has a location and devices which provide some services, a user who uses his/her device to request such services at this location that has a specific activity carried out in a specific moment. However, for these relationships, it is required to establish linguistic specifications with threshold values (often defined by the domain expert) to extract the concepts instances that satisfies the selected values. For instance, according to user requirements, the relation \u0026ldquo;distance in\u0026rdquo; that relates the user concept to the location concept can be expressed using three different linguistic variables: located in, close to, far from. A close place to some users is not close for another, thus, the borderline between these terms is vague and overlap between them could be exist. Therefore, the definition for these linguistic terms should be fuzzified to meet the domain requirements. Moreover,\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eb) Phase 2: defining the ontology\u0026rsquo;s elements.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eHere, domain experts and ontology engineers collaboratively work to provide a precise distinction between fuzzy related information and crisp information. As a result, the knowledgebase will be partitioned into two different parts: precise information (crisp elements) and fuzzy rough related information. The crisp elements will be identified to acquire the precise information by which the targeted domain will be modeled. For the needs of this demonstration and given the publication\u0026rsquo;s length and clarity considerations, we limit the ontology to the following elements. We distinguish among six main entities: User, Location, PersonalStatus, Environment, Activity, and Action. All these elements together define the 5Ws questions related to user\u0026rsquo;s context: Who, What, When, Where, and Why. Figure\u0026nbsp;5 shows the initial layout of the constructed ontology with the identified concepts and sub concepts.\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eUser: this class represents a single unique user who has some properties such as profile, calendar, and mobility situation. It is responsible for representing the user as an observed entity in the environment. A specific user represents a specific role according to the targeted domain. For instance, a user can be a tourist, patient, visitor, lecturer, shopper, etc.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eEnvironment: this class represents an organized hierarchy of indoor and outdoor locations, and their generic and specific features. For example, in the office environment, offices, meeting rooms, lecture rooms, conference rooms, kitchen, toilets, etc., are examples of locations in an environment. An environment can have some associated weather measurements such as Humidity, Temperature, Lighting, and Pressure.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eAction: actions can be seen as an atomic event performed by the user with a timestamp, e.g., EnterBuilding, OpenDoor, WalkBy, TurnOnLight, etc.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eActivity: activity can be considered as a single or composite set of actions with an \u0026ldquo;inherent intend\u0026rdquo; with a StartDateTime and EndDateTime. For example, AttendinMeeting, DoingPresentation, MakingCoffee, ScheduledEvent, VisitingLocation, etc. An activity is a set of weighted, compulsory and/or optional actions. Some activities could be divided into more specific sub smaller activities such as Lecturing activity that can be either GiveLecture or AttendLecture.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eLocation: this class can be any indoor or outdoor location in which a specific user is located in, nearby, or far from. Indoor locations can be a public building such as a hospital, shopping mall, restaurant, department, etc. or a private building such as a home, a room (lecture room, meeting room, conference room), etc. Outdoor locations include a metro, park, street, train, terrace, etc.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003ePersonalStatus: the personal status of a user represents his status at a specific moment. Status can be Available, OnLeave, Away, Busy, etc. Figure\u0026nbsp;6 depicts the different six concepts with their specifications represented in Prot\u0026eacute;g\u0026eacute;.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eFuzzy Datatypes and Fuzzy Concrete Roles (data properties)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003etypical data properties in the original ontology can be transformed into fuzzy datatypes with ranges expressed using data range expressions such as (double 0.0] and double [\u0026thinsp;\u0026lt;\u0026thinsp;=\u0026thinsp;1000.0]) for \u003cem\u003ehasDistance\u003c/em\u003e data property range. Fuzzy concrete roles are defined in FuzzyOWL2 by setting its range datatype to one of the predefined fuzzy datatypes. An annotation example in OWL2 for the defined datatype \u003cem\u003eCloseToDistance\u003c/em\u003e is as follows\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n\u003cp\u003e\u0026lt;fuzzyOwl2 fuzzyType=\\\"datatype\\\"\u0026gt; \u0026lt;Datatype type=\\\"trapezoidal\\\" a=\\\"25\\\" b=\\\"50\\\" c=\\\"150\\\" d=\\\"450\\\" /\u0026gt; \u0026lt;/fuzzyOwl2\u0026gt;\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eListing 1: Annotation for a New Fuzzy Datatype CloseToDistance Using Trapezoidal Modifier\u003c/p\u003e\n\u003cp\u003eThe fuzzy datatypes defined in the user\u0026rsquo;s context fuzzy rough ontology are:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cem\u003eStillMobility, MovingMobility\u003c/em\u003e: these two fuzzy datatypes used to represent user\u0026rsquo;s situation, i.e., whether he is moving with a specific speed (km/h) or he is still in his place. The concrete role User.\u003cem\u003ehasMobility\u003c/em\u003e indicates his situation in that particular time.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cem\u003eLocatedInDistance, CloseToDistance, FarFromDistance\u003c/em\u003e: are used to approximate the distance of the user from a specific place (in meters). The concrete role User.\u003cem\u003ehasDistance\u003c/em\u003e indicates the distance in meters between the user and a specific location.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cem\u003eDryHumidity, NormalHumidity, HumidHumidity\u003c/em\u003e: are used to model humidity (in percentage). The concrete role Location.\u003cem\u003ehasHumidity\u003c/em\u003e indicates the humidity level of a specific Location.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cem\u003eColdTemperature, WarmTemperature, HotTemperature\u003c/em\u003e: are used to measure temperature (in Celsius degrees). The concrete role Location.\u003cem\u003ehasTemperature\u003c/em\u003e indicates the temperature of a specific Location.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cem\u003eDarkLighting, DimLighting, NormalLighting, BrightLighing\u003c/em\u003e: are identified to measure lighting (in lumens). The concrete role Location.\u003cem\u003ehasLighting\u003c/em\u003e indicates the amount of light getting out from a bulb in a specific Location within an environment.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cem\u003eShortDuration, MediumDuration, LongDuration\u003c/em\u003e: are used to represent duration (in minutes). The concrete role Activity.\u003cem\u003ehasDuration\u003c/em\u003e indicates the duration of a specific activity.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cem\u003eCloseToTime, FarFromTime\u003c/em\u003e: are used to approximate the duration of time (in minutes) between two different activities/actions. the concrete roles {Activity, Action}. \u003cem\u003eCloseToTime\u003c/em\u003e indicates the duration of time between activities/actions. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e depicts the fuzzy datatypes and fuzzy concrete roles (data properties) identified using Prot\u0026eacute;g\u0026eacute; (partial). Note that, the figure shows both the identified data properties including fuzzy and non-fuzzy ones.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eFuzzy Abstract Roles (Fuzzy Object Properties).\u003c/strong\u003e By assigning a fuzzy membership value, the object properties in the original ontology can be converted to fuzzy abstract roles. Some of these roles in the developed ontology are:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eUser-\u003cem\u003eIsLocatedIn\u003c/em\u003e-Location: Represents the location of a user in a given moment. A fuzzy degree can approximate the degree of which a specific user is located in a specific location.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eUser-\u003cem\u003eAttend\u003c/em\u003e -Event: Identifies a given user who attends an event. An even can be an appointment in the user\u0026rsquo;s calendar.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eUser-\u003cem\u003ePerform\u003c/em\u003e-Activity: Specifies which user performs an Activity. Given a fuzzy degree here, represents the level of uncertainty about whether the user performs the specified activity.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eUser-\u003cem\u003ePerformAction\u003c/em\u003e-Action: Specifies which User performs an Action. Given a fuzzy degree here, represents the level of uncertainty about whether the user performs the specified action.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eUser-\u003cem\u003eHasStatus\u003c/em\u003e-PersonalStatus: Indicates a personal status of any user in certain moment. For example, a user can be available, on-leave, away, and busy.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eUser-\u003cem\u003eParticipateIn\u003c/em\u003e-Activity: Specifies a given user who participate in a specific activity. A fuzzy degree can approximate the degree of which a specific user is participating in a specific activity.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eActivity-\u003cem\u003eHappenIn\u003c/em\u003e-Location Represents the location of an activity in a given moment. A fuzzy degree can approximate the degree of which a specific activity is located in a specific location.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eAction-\u003cem\u003eActionHappenIn\u003c/em\u003e-Location Represents the location of an action in a given moment. A fuzzy degree can approximate the degree of which a specific action is located in a specific location. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e shows some of the identified fuzzy/crisp object properties in Prot\u0026eacute;g\u0026eacute;.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eIt is worth noting that in the previously identified elements, there are no explicit vague concepts, and the vagueness (the lack of precise boundaries between vague attributes) is occurred because of some relations and attributes.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ec) Phase 3: approximating the vague fuzzy concepts/sets using linguistic modifiers/hedges through fuzzy rough sets (approximators).\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eLinguistic modifiers (also referred to as linguistic hedges) are specific type of linguistic expressions like very, extremely, more or less, quiet. While applied to adjectives, linguistic hedges allow us to express an emphasis we impose on the corresponding properties. They can be considered as special expressions by which the degree of membership of fuzzy datatype/relation could be modified. hedges such as very, extremely, definitely, more or less, roughly, almost, possible, etc., are utilized to describe the vague properties of fuzzy concepts. These modifiers are modeled by means of the construction of upper and lower approximations of the identified fuzzy concepts and relations. For example, given the fuzzy datatype property \u003cem\u003eCloseToDistance\u003c/em\u003e between (User, Location), the fuzzy modifier \u003cem\u003eVery\u003c/em\u003e is identified to modify the value of the membership function of that datatype and hence, the newly identified \u003cem\u003eVeryCloseToDistance\u003c/em\u003e datatype makes the user not only \u003cem\u003eClose\u003c/em\u003e to a specific location, but \u003cem\u003eVeryClose\u003c/em\u003e to that location. Listing 2 expresses this modification in OWL2.\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n\u003cp\u003e\u0026lt;fuzzyOwl2 fuzzyType= \u0026lsquo;\u0026lsquo;datatype\u0026rdquo;\u0026gt; \u0026lt;Datatype type= \u0026lsquo;\u0026lsquo;modified\u0026rdquo; modifier= \u0026lsquo;\u0026lsquo;very\u0026rdquo; base= \u0026lsquo;\u0026lsquo;CloseToDistance\u0026rdquo;/\u0026gt; \u0026lt;/fuzzyOwl2\u0026gt;\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eListing 2: Datatype \u0026ldquo;CloseToDistance\u0026rdquo; modified by \u0026ldquo;very\u0026rdquo; modifier.\u003c/p\u003e\n\u003cp\u003eLinguistic fuzzy rough sets (also called fuzzy necessity and fuzzy possibility) will be used to tune the membership function values according to users\u0026rsquo; preferences and requirements. This could be achieved through using (1) and (2). For example, the term \u0026ldquo;close\u0026rdquo; in the fuzzy relation \u003cem\u003eIsLocatedIn\u003c/em\u003e can be expressed by the formula\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e𝑅(𝑥, 𝑦)\u0026thinsp;=\u0026thinsp;max (0, min (1, 3.5 -\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{\\left|x-y\\right|}{100}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e))\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eAnd fuzzy membership function:\u003c/p\u003e\n\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equa\" class=\"mathdisplay\"\u003e$${\\mu }\\left(\\text{c}\\text{l}\\text{o}\\text{s}\\text{e}\\right)= \\left\\{\\begin{array}{c}\\frac{x-0}{500-0} 0\\le x\\le 500\\\\ 1 500\u0026lt;x\\le 1000\\\\ \\frac{1500-x}{1500-1000} 1000\u0026lt;x\\le 1500\\\\ 0 x\u0026gt;1500, x\u0026lt;0\\end{array}\\right.$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAs shown from the previous function, a place that distant 600M is close to the user with 1 confidence value (the value of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\)\u003c/span\u003e\u003c/span\u003e). However, if the user decided to discover the places that are \u0026ldquo;very\u0026rdquo; close, this value will be tuned to be .8 for the same distance using the lower approximation. The lower approximation of the fuzzy term \u0026ldquo;close\u0026rdquo; can be calculated to find the new membership value for the same place when it required to be considered as \u0026ldquo;very close\u0026rdquo;. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e illustrates the membership function values for the \u0026ldquo;close\u0026rdquo; and \u0026ldquo;VeryClose\u0026rdquo; distances.\u003c/p\u003e\n\u003cp\u003eThe second fuzzy element is the attribute \u0026ldquo;temperature\u0026rdquo;. The fuzzy term \u0026ldquo;Warm\u0026rdquo; that represents one of the weather conditions can be expressed using\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e𝑅(𝑥, 𝑦)\u0026thinsp;=\u0026thinsp;min (1, max (0, 2 -\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{\\left|x-y\\right|}{2}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e))\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eand the following membership function:\u003c/p\u003e\n\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equb\" class=\"mathdisplay\"\u003e$${\\mu }\\left(\\text{W}\\text{a}\\text{r}\\text{m}\\right)= \\left\\{\\begin{array}{c} \\frac{x-0}{19-0} 0\\le x\\le 19\\\\ 1 19\u0026lt;x\\le 24\\\\ \\frac{28-x}{28-24} 24\u0026lt;x\\le 28\\\\ 0 x\u0026gt;28, x\u0026lt;0\\end{array}\\right.$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAs seen from the function, the temperature degree 14 is considered warm with .7 confidence degree. However, the same temp. degree is considered \u0026ldquo;very warm\u0026rdquo; with just .6 confidence value. It is worth noting that the linguistic modifier \u0026ldquo;very\u0026rdquo; again used to tune this value using the lower approximation of the fuzzy term \u0026ldquo;warm\u0026rdquo;. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e depicts the difference between the confidence values of the term \u0026ldquo;Warm\u0026rdquo; and \u0026ldquo;very Warm\u0026rdquo; temperature.\u003c/p\u003e\n\u003cp\u003eAnother fuzzy attribute in the constructed ontology is the \u0026ldquo;user mobility\u0026rdquo; by which the mobility of a specific user, throughout estimating his/her speed, is evaluated. The following membership function illustrates the confidence values of the user mobility according to the detected speed.\u003c/p\u003e\n\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equc\" class=\"mathdisplay\"\u003e$${\\mu }\\left(\\text{S}\\text{t}\\text{i}\\text{l}\\text{l}\\right)= \\left\\{\\begin{array}{c} 1 x\u0026lt;2\\\\ \\frac{5-\\text{x}}{3} 2\u0026lt;x\\le 5\\\\ 0 x\u0026gt;5\\end{array}\\right.$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eFor example, if the user is moving with 3 km/h speed, we can say that he is still with .7 confidence value. However, in some cases, we need to discover the \u0026ldquo;possibility\u0026rdquo; that this user is \u0026ldquo;still\u0026rdquo;. In such case, the upper approximation of this fuzzy set needs to be calculated using the upper approximation formula (table1).\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e depicts how values of the membership function of different speeds were changed when the \u0026ldquo;possibility\u0026rdquo; of user movement is considered. For instance, the truth value is increased from .5 to .8 when checking whether a user with 3.5 km/h speed is \u0026ldquo;possibly\u0026rdquo; still rather than \u0026ldquo;just\u0026rdquo; still.\u003c/p\u003e\n\u003cp\u003eThe last two fuzzy relations are \u003cem\u003eIsScheduledAt/ IsOccurredAt.\u003c/em\u003e As previously explained, these two relations express the time approximation of a specific event/action to be started/occurred. The following is the membership function that can be used to calculate the confidence value of the difference (in minutes) between two specific event, activity or action.\u003c/p\u003e\n\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equd\" class=\"mathdisplay\"\u003e$${\\mu }\\left(\\text{C}\\text{l}\\text{o}\\text{s}\\text{e}\\right)= \\left\\{\\begin{array}{c} 1 x\u0026lt;30\\\\ \\frac{50-x}{20} 30\u0026lt;x\\le 50\\\\ 0 x\u0026gt;50\\end{array}\\right.$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAs shown, the 43 minutes difference between two activities makes them close with .4 confidence level. On the other hand, this value is increased up to .6 when to check whether these two activities are \u0026ldquo;possibly\u0026rdquo; close to each other (using the upper approximation). Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e shows the difference between these membership values considering \u0026ldquo;close\u0026rdquo; and \u0026ldquo;possibly close\u0026rdquo; fuzzy terms.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ed) Phase 4: reusing existing ontology elements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ein the constructed ontology, as illustrated in the concepts taxonomy, there are some general concepts such as time and location that can be reused from the publically available ontologies instead of rebuilding them from the scratch. [\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e] [\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ee) Phase 5: formalization of the constructed ontology\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn this use case, OWL2 could be selected as the formalism language to represent the designed ontology model. Ontology editors such as the fuzzy-OWL prot\u0026eacute;g\u0026eacute; extension could be utilized in this phase. Prot\u0026eacute;g\u0026eacute; provides an easy user-friendly tool to visually implement the designed ontologies and allows for automatic generation of the code in different languages such as OWL and RDF. For example, Syntax and semantics of RDF are extended to support real numbers of the interval [0,1] to be expressed as degrees subjects, objects, and predicates [\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e]. In addition, there are a set of fuzzy extensions of description logics as in [\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e] that could be utilized to enable this transformation process. Bobillo et al. [\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e], and Nilavu and Sivakumar [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e] introduced a concrete methodology to formalize fuzzy and fuzzy rough ontologies using OWL2 annotation properties. It is worth noting that different ontology formalism languages vary from each other in terms of characteristics, rules, and capabilities they have. There is no a standard mechanism to evaluate these languages regarding their strength and weakness in representing a specific ontology element. Therefore, the formalism language should be chosen according to constructed ontology\u0026rsquo;s requirements.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ef) Phase 6: validation of the constructed ontology\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe validation results serve as proof of the usefulness of the developed fuzzy rough ontology. Although the consistency of the constructed ontology could be evaluated by the \u003cem\u003efuzzyDL\u003c/em\u003e reasoner, the other features should be subjectively examined by the ontology engineers, domain experts, and ontology users who have been involved in the development process. Specifically, the validation results are presented in the following:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eThe developed fuzzy rough ontology is correct. The vagueness that is reflected in all identified fuzzy elements is precisely captured and implemented with correctly identified fuzzy rough sets. In addition, the links between the crisp and fuzzy elements have been accurately identified. In order to verify the constructed ontology, another domain expert could be consulted.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe developed ontology is consistence. Even though the consistency characteristic is often evaluated by the fuzzy description logic reasoner, both structure and content don\u0026rsquo;t have any controversial definitions regarding the domain vagueness in the developed ontology.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe developed ontology is complete. All the constructed elements have precisely captured the vagueness meaning identified in the different phases and covered all the knowledge requirements. Here, additional domain experts could be consulted to ensure that the identified crisp parts do not contain any vague meaning.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe developed ontology is understandable. Since that all the defined terms are self-explanatory, the constructed ontology can be easily understood by domain experts, ontology engineers and the intended users.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe developed ontology is conciseness. All the identified elements are accurately approximating the degree of vagueness in an intuitive way.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"5. Discussion and conclusion","content":"\u003cp\u003eThe proposed methodology can be considered as a set of activities by which a fuzzy rough ontology is built in a logic order. The essential goal of this methodology is to provide a methodological guideline to follow in order to construct this type of ontologies, thus ensuring an enhanced performance comparing to intuitive ontology constructing works. As stated in the introduction, The FUZRUF-onto is the first methodology that combines fuzzy set and rough set theories to precisely identify context dependent characteristics of objects, thus, express users preferences more accurately through tuning the confidence level of the inferred context. As shown in the practical use case, the context ontology has been successfully constructed following the step-by-step guideline provided by the FUZRUF-onto phases. During the development process, each of these phases has been set with precise purposes and to do list. It is clear that using the FUZRUF-onto, both efficiency and accuracy can be enhanced in fuzzy rough ontologies development process.\u003c/p\u003e\n\u003cp\u003eFor theoretical methodology, it is quite difficult to perform a quantitative and comparison analysis with existing methodologies. Reviewing the relevant literature, it has been noticed that there is a lack of a well-established quantitative analysis and evaluation to compare and test new developed methodologies with other existing ontology methodologies [\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e]. For example, METHONTOLOGY [\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e], the well-known crisp ontology methodology does not include any sort of evaluation. Likewise, although they proved their applicability by providing some experimental scenarios and use cases, some other works such as NeON [\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e], Diligent [\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e] and [\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e] have not provided any rigorous evaluation. Due to the subjective nature of this field, current research community just accepts the way an ontology development methodology is introduced even with the exclusion of the evaluation part. Similarly, as the developed methodology was accompanied with a detailed description of the vague knowledge and an explicit interpretation of each phase, it is expected to provide an effective enhancement in the fuzzy rough ontology development process due to the following reasons:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eComparing with the existing non-methodological ontology development processes in which ontology engineers build the ontology based on their preferences and intuition, the developed methodology provides them a well-established development process. The only overhead that could be introduced in this type of methodologies is the time required to understand, learn, and practice the methodology phases.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe proposed methodology focuses on the knowledge representation (including both crips and fuzzy knowledge) at the conceptual level rather than the actual technical representation. This allows developers to focus on the development process without worrying about the formalization process.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eAs stated earlier, the detailed description of the vague knowledge and the explicit interpretation of the fuzzy degrees, and their approximations using rough sets ensures that everybody involved in the development process, including domain experts and ontology engineer, can define the vagueness meaning in an easier, more complete and more accurate manner.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe detailed fuzzy rough ontology elements identification phases allow the constructed ontology to become sharable and reusable by other developers in different domains.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eAs the developed methodology categorize the targeted domain knowledge into two different parts: crisp information and fuzzy information, ontology engineers can precisely identify the borderline between them, thus find different approaches to model them. For the crisp part, existing ontology development methodologies could be utilized which allows engineers to focus on the fuzzy part.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe proposed methodology can be considered as the first of its type of methodological guideline for building fuzzy rough ontologies from the scratch. Starting from identifying the motivation, going through defining and approximating the fuzzy sets elements, reusing other external ontology elements and ending up validating the designed ontology.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eFollowing the methodology phases, developers can build a fuzzy rough ontology in which the fuzzy sets are approximated to tune the membership function values according to users\u0026rsquo; preferences and requirements. This could be achieved through using linguistic fuzzy rough sets (fuzzy necessity and fuzzy possibility) modifiers such as extremely, roughly, very, exactly, almost, possible, potential, rather, etc.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eI. Jurisica, J. Mylopoulos, and E. Yu, \u0026ldquo;Ontologies for Knowledge Management: An Information Systems Perspective,\u0026rdquo; \u003cem\u003eKnowl. Inf. Syst.\u003c/em\u003e, vol. 6, pp. 380\u0026ndash;401, 2004.\u003c/li\u003e\n\u003cli\u003eR. Studer, V. R. Benjamins, and D. Fensel, \u0026ldquo;Knowledge engineering: principles and methods-Source link,\u0026rdquo; 1998.\u003c/li\u003e\n\u003cli\u003eD. Nilavu and R. Sivakumar, \u0026ldquo;Knowledge Representation Using Type-2 Fuzzy Rough Ontologies in Ontology Web Language,\u0026rdquo; \u003cem\u003eFuzzy Inf. Eng.\u003c/em\u003e, vol. 7, no. 1, pp. 73\u0026ndash;99, 2015.\u003c/li\u003e\n\u003cli\u003eT. R. 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Carmen Su\u0026aacute;rez-Figueroa, \u0026ldquo;NeOn Methodology for Building Ontology Networks: a Scenario-based Methodology.\u0026rdquo;\u003c/li\u003e\n\u003cli\u003eH. Sofia Pinto, C. Tempich, D. Vrandeči, S. Pinto, and Y. Sure, \u0026ldquo;The DILIGENT knowledge processes,\u0026rdquo; \u003cem\u003eArtic. J. Knowl. Manag.\u003c/em\u003e, 2005.\u003c/li\u003e\n\u003cli\u003eR. N. Carvalho, K. B. Laskey, and P. C. G. da Costa, \u0026ldquo;Uncertainty modeling process for semantic technology,\u0026rdquo; \u003cem\u003ePeerJ Comput. Sci.\u003c/em\u003e, vol. 2016, no. 8, pp. 1\u0026ndash;36, 2016.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Fuzzy sets, Fuzzy theory, Rough sets, Fuzzy ontologies, Ontology engineering, Knowledge representation","lastPublishedDoi":"10.21203/rs.3.rs-3927799/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3927799/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNowadays, semantic web technologies play a crucial role in knowledge representation paradigm. With the raise of imprecise and vague knowledge, there is an upsurge demand in applying a concrete well-established procedure to represent such knowledge. Ontologies, particularly fuzzy ontologies are increasingly applied in application scenarios in which handling of vague knowledge is significant. However, such fuzzy ontologies utilize fuzzy set theory to provide quantitative methods to manage vagueness. In various cases of real-life scenarios, people need to express their everyday requirements using linguistic adverbs such as very, exactly, mostly, possibly, etc. The aim is to show how fuzzy properties can be complemented by Rough Set methods to capture another type of imprecision caused by approximation spaces. Rough sets theory offers a qualitative approach to model such vagueness via describing fuzzy properties at multiple levels of granularity using approximation sets. Using rough-set theory, each fuzzy concept is represented by two approximations. The lower approximation \u003cem\u003ePL(C)\u003c/em\u003e consists of a set of fuzzy properties that are definitely observable in the concept. The upper approximation \u003cem\u003ePU(C)\u003c/em\u003e on the other hand contains fuzzy properties that are possibly associated with the concept but may not be observed. This paper introduces a methodology named FUZRUF-onto methodology, which is a formal guidance on how to build fuzzy rough ontologies from scratch using extensive research in the area of fuzzy rough combination. Fuzzy set and rough set theories are applied to capture the inherently fuzzy relationships among concepts expressed by natural languages. The methodology provides a very good guideline for formally constructing fuzzy rough ontologies in terms of completeness, correctness, consistency, understandability, and conciseness. To explain how the FUZRUF-onto works, and demonstrate its usefulness, a practical step by step example is provided.\u003c/p\u003e","manuscriptTitle":"FUZRUF-onto: a Methodology to Develop Fuzzy Rough Ontologies","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-06 16:33:25","doi":"10.21203/rs.3.rs-3927799/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"e8a745ab-9b1b-4b86-88ac-25cdfb4f4b01","owner":[],"postedDate":"February 6th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-02-06T16:33:25+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-06 16:33:25","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3927799","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3927799","identity":"rs-3927799","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}