Arbitrary Coupled Trapezoidal Fully Fuzzy Sylvester Matrix Equation

Arbitrary Coupled Trapezoidal Fully Fuzzy Sylvester Matrix Equation | 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 Arbitrary Coupled Trapezoidal Fully Fuzzy Sylvester Matrix Equation Ahmed Elsayed, Nazihah Ahmad, Ghassan Malkawi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-579719/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 There are many applications where couple of Sylvester matrix equations (CSME) are required to be solved simultaneously, especially in analyzing the stability of control systems. However, there are some situations in which the crisp CSME are not well equipped to deal with the uncertainty problem during the process of stability analysis in control system engineering. Thus, in this paper a new method for solving a coupled trapezoidal fully fuzzy Sylvester matrix equation (CTrFFSME) with arbitrary coefficients is proposed. The arithmetic fuzzy multiplication operation is applied to convert the CTrFFSME into a system of non-linear equations. Then the obtained non-linear system is reduced and converted to a system of absolute equations where the fuzzy solution is obtained by solving that system. The proposed method can solve many unrestricted fuzzy systems such as Sylvester and Lyapunov fully fuzzy matrix equations with triangular and trapezoidal fuzzy numbers. We illustrate the proposed methods by solving numerical example. Applied Mathematics Arbitrary fuzzy systems Couple Sylvester matrix equations Near-zero fuzzy numbers Trapezoidal fuzzy numbers Trapezoidal fuzzy multiplication Full Text 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. 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-579719","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":34383877,"identity":"06e6cf09-c56b-4865-bfc6-a8bd09813a70","order_by":0,"name":"Ahmed Elsayed","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-9255-200X","institution":"Applied Technology High School - Abu Dhabi Campus: Applied Technology High School","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Ahmed","middleName":"","lastName":"Elsayed","suffix":""},{"id":34383878,"identity":"45ec460b-c2cc-4f22-98a5-426027947261","order_by":1,"name":"Nazihah Ahmad","email":"","orcid":"","institution":"Universiti Utara Malaysia","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Nazihah","middleName":"","lastName":"Ahmad","suffix":""},{"id":34383879,"identity":"25a95b37-b57a-4692-bf63-7c0888eee4b8","order_by":2,"name":"Ghassan Malkawi","email":"","orcid":"","institution":"Higher Colleges of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Ghassan","middleName":"","lastName":"Malkawi","suffix":""}],"badges":[],"createdAt":"2021-06-01 12:12:40","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-579719/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-579719/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":13659602,"identity":"2839261d-a88a-4e88-bb78-e7ad76bda595","added_by":"auto","created_at":"2021-09-17 10:20:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":413157,"visible":true,"origin":"","legend":"","description":"","filename":"Paper6XYpartBSquarecitation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-579719/v1_covered.pdf"},{"id":11538870,"identity":"9a9dbeee-69db-44df-a66b-d5085fa77bb0","added_by":"auto","created_at":"2021-07-16 16:57:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":409528,"visible":true,"origin":"","legend":"","description":"","filename":"Paper6XYpartBSquarecitation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-579719/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"Arbitrary Coupled Trapezoidal Fully Fuzzy Sylvester Matrix Equation","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-579719/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"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":"Arbitrary fuzzy systems, Couple Sylvester matrix equations, Near-zero fuzzy numbers, Trapezoidal fuzzy numbers, Trapezoidal fuzzy multiplication","lastPublishedDoi":"10.21203/rs.3.rs-579719/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-579719/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThere are many applications where couple of Sylvester matrix equations (CSME) are required to be solved simultaneously, especially in analyzing the stability of control systems. 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