{"paper_id":"09ee553d-cd24-43d4-b343-4414fcc5a5b4","body_text":"An algorithm for finding a minimal solution to fuzzy relation inequalities with addition-min composition | 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 An algorithm for finding a minimal solution to fuzzy relation inequalities with addition-min composition Xue-Ping Wang, Xiao Mi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-581893/v2 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 2 posted 5 You are reading this latest preprint version Show more versions Abstract We first show a sufficient and necessary condition that a solution of fuzzy relation inequalities with addition-min composition is a minimal one. We then prove that for every solution of the fuzzy relation inequalities there exists a minimal solution that is less than or equal to the solution in a very different way. We finally give an algorithm to find a minimal solution for a given solution, which is illustrated by numerical examples. Fuzzy relational inequality Addition-min composition Minimal solution Algorithm Full Text Cite Share Download PDF Status: Under Revision Version 2 posted Editorial decision: Minor Revision 22 Oct, 2022 Reviewers agreed at journal 21 Aug, 2022 Reviewers invited by journal 24 Feb, 2022 Editor assigned by journal 12 Dec, 2021 First submitted to journal 07 Oct, 2021 You are reading this latest preprint version Show more versions 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-581893\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[{\"code\":1,\"date\":\"2021-07-01 14:05:34\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research 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