A Fully Fuzzy Multi-Objective Linear Programming Model for Roof Gardening Using Trapezoidal Fuzzy Numbers

A Fully Fuzzy Multi-Objective Linear Programming Model for Roof Gardening Using Trapezoidal Fuzzy Numbers | 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 Fully Fuzzy Multi-Objective Linear Programming Model for Roof Gardening Using Trapezoidal Fuzzy Numbers Revathi Annamalai Natarajan, Nachiappan Angappan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6522318/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 5 You are reading this latest preprint version Abstract Urban roof gardening has emerged as a sustainable solution to address food security and envi- ronmental challenges. However, the optimization of crop selection and resource allocation in roof gardening is complicated by uncertainty in key factors such as resource availability and crop yield. In this study, a fully fuzzy multi-objective linear programming (FFMOLP) model is developed to optimize crop selection and resource allocation under uncertainty. Trapezoidal fuzzy numbers are used to model both the left-hand side (LHS) and right-hand side (RHS) of the constraints. A real-world numerical example demonstrates the applicability of the proposed model, highlighting its ability to handle uncertain conditions effectively. Fuzzy linear programming Multi-objective optimization Roof gardening Trapezoidal fuzzy numbers Sustainable agriculture Full Text Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Major revisions 09 Mar, 2026 Reviewers agreed at journal 15 May, 2025 Reviewers invited by journal 15 May, 2025 Editor assigned by journal 26 Apr, 2025 First submitted to journal 25 Apr, 2025 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. 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-6522318","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":457072751,"identity":"f3b66352-3d57-40cb-904a-85a4ac59ff0f","order_by":0,"name":"Revathi Annamalai Natarajan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVRIiWNgGAWjYBCDBDb59x8fABk8fETqMEhgY0gwNgBpYSNaC9AiMwkQk6AW/tm9Dx/z1PzJ42M4kFb5NcdOho2B+eGjG3i0SNw5bmzMc8ygmI2x4dht2W3JQIexGRvn4LPmRhqb5Aw2g8Q2Zsa225LbmIFaeNik8WmRv5HG/nPGP6AWNma2Yslt9YS1GABtYfjYBtTCw8bG+HHbYcJaDG+kMUt87DNObJPgYZZm3HacB2gbfr/I3Uhj/JDwTS5x/gwexo8/t1Xb87M3P3yM1/vIgJkHTBKrHAQYf5CiehSMglEwCkYMAABR5UDzIWKX4QAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-1462-8790","institution":"SRM Valliammai Engineering College","correspondingAuthor":true,"prefix":"","firstName":"Revathi","middleName":"Annamalai","lastName":"Natarajan","suffix":""},{"id":457072752,"identity":"d6a53c2d-5b90-4820-9206-3b3259f650b9","order_by":1,"name":"Nachiappan Angappan","email":"","orcid":"","institution":"NIT-Trichy: National Institute of Technology Tiruchirappalli","correspondingAuthor":false,"prefix":"","firstName":"Nachiappan","middleName":"","lastName":"Angappan","suffix":""}],"badges":[],"createdAt":"2025-04-24 15:50:56","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6522318/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6522318/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83152236,"identity":"3b6bdcb6-7cf0-4e3a-ab64-306c2f380dcc","added_by":"auto","created_at":"2025-05-20 14:03:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":293257,"visible":true,"origin":"","legend":"","description":"","filename":"FFMOLPPaper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6522318/v1_covered_78f7ea03-e660-4fc5-8d56-d3e29a92f1fb.pdf"}],"financialInterests":"","formattedTitle":"A Fully Fuzzy Multi-Objective Linear Programming Model for Roof Gardening Using Trapezoidal Fuzzy Numbers","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"water-resources-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"warm","sideBox":"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)","snPcode":"11269","submissionUrl":"https://submission.nature.com/new-submission/11269/3","title":"Water Resources Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Fuzzy linear programming, Multi-objective optimization, Roof gardening, Trapezoidal fuzzy numbers, Sustainable agriculture","lastPublishedDoi":"10.21203/rs.3.rs-6522318/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6522318/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Urban roof gardening has emerged as a sustainable solution to address food security and envi-\nronmental challenges. 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