A Total Ranking of Linear Diophantine Fuzzy Numbers with Multi-criteria Decision Making

A Total Ranking of Linear Diophantine Fuzzy Numbers with Multi-criteria Decision Making | 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 Research Article A Total Ranking of Linear Diophantine Fuzzy Numbers with Multi-criteria Decision Making Abirami K M, Srikanth R, Dhanasekaran P This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3400568/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract In this paper, the class of linear Diophantine fuzzy numbers (LDFNs) is divided into three main subclasses in which four different score functions namely improved score function (ISF), improved quadratic score function (IQSF), improved expectation score function (IESF) and non-linear score function (NLSF) are introduced and some of its important properties are proved and validated by illustrative examples. Further a total order relation is introduced based on three subclasses on LDFNs to rank any two LDFNs and multi-criteria decision-making (MCDM) problem is used to validate the proposed methods and compared with some of the existing methods under linear Diophantine fuzzy environment. Linear Diophantine fuzzy numbers Improved score function Improved quadratic score function Improved expectation score function Non-linear score function Multi-criteria decision making. Full Text Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Major Revision 11 Dec, 2023 Reviewers agreed at journal 03 Nov, 2023 Editor assigned by journal 04 Oct, 2023 First submitted to journal 30 Sep, 2023 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. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3400568","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":246036238,"identity":"0fb3ce59-29a5-407b-a4ac-29fc64606e5d","order_by":0,"name":"Abirami K M","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABE0lEQVRIie2PMUvDQBTHXzh4XU5dr0STr9AQCF2sX6XHgV10dyghEEinOisO+QRCppsjhZuErAFdSsBNyCTpoHilDlYv4Ohwv+G94f4/3v8ALJb/CHOS7fT0wP0XNKS/KyEAwf1ov7JbPPml9HF0l2bt5mI8u19Uat1B7Pv5ct3CfAKHbmI+8vyQ3i4lu5SPYhBSWAWFGoQMlAA8Ls1nap7CwVYpBboApVMg6rZYArKp0fC14rxLNouqBoe62FmeIengo18ZaYXoK9OoFsgoEJ4oROZk/Uqg/0JOJAtk3UQuHa1Eoc5xzK8F7VO8p0XjvMrYjyr+Muyu4tM8VaRu3yaef2NWfvb82jpM/5K3WCwWi5lPfb5UnuLQRpMAAAAASUVORK5CYII=","orcid":"","institution":"SASTRA Deemed University: Shanmugha Arts Science Technology and Research Academy","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Abirami","middleName":"K","lastName":"M","suffix":""},{"id":246036239,"identity":"4b1f0684-9932-4217-ac96-9130dc51857f","order_by":1,"name":"Srikanth R","email":"","orcid":"","institution":"SASTRA Deemed University: Shanmugha Arts Science Technology and Research Academy","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Srikanth","middleName":"","lastName":"R","suffix":""},{"id":246036240,"identity":"ae9b45c0-dfc6-4d71-8a0a-a192512022ee","order_by":2,"name":"Dhanasekaran P","email":"","orcid":"https://orcid.org/0000-0003-3134-1898","institution":"SASTRA Deemed University: Shanmugha Arts Science Technology and Research Academy","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Dhanasekaran","middleName":"","lastName":"P","suffix":""}],"badges":[],"createdAt":"2023-09-30 11:35:02","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3400568/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3400568/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":45972999,"identity":"a41dacb7-70ae-4532-84ef-a6f8e540d4c0","added_by":"auto","created_at":"2023-11-07 03:31:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":634187,"visible":true,"origin":"","legend":"","description":"","filename":"LDFN.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3400568/v1_covered_cdb9b655-bb3c-44ee-81ea-727835c14a3e.pdf"}],"financialInterests":"","formattedTitle":"A Total Ranking of Linear Diophantine Fuzzy Numbers with Multi-criteria Decision Making","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"soft-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"soco","sideBox":"Learn more about [Soft Computing](https://www.springer.com/journal/500)","snPcode":"500","submissionUrl":"https://submission.nature.com/new-submission/500/3","title":"Soft Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Linear Diophantine fuzzy numbers, Improved score function, Improved quadratic score function, Improved expectation score function, Non-linear score function, Multi-criteria decision making.","lastPublishedDoi":"10.21203/rs.3.rs-3400568/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3400568/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, the class of linear Diophantine fuzzy numbers (LDFNs) is divided into three main subclasses in which four different score functions namely improved score function (ISF), improved quadratic score function (IQSF), improved expectation score function (IESF) and non-linear score function (NLSF) are introduced and some of its important properties are proved and validated by illustrative examples. 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