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This paper constructs analytical and numerical methods for solving a couple of trapezoidal fully fuzzy Sylvester matrix equations (CTrFFSMEs) to overcome the drawbacks of the existing crisp methods. In developing these new methods, fuzzy arithmetic multiplication is applied on the CTrFFSME to transform it into an equivalent system of four CSMEs. Then, the fuzzy solution is obtained analytically by the fuzzy matrix vectorization method and numerically by gradient and least square methods. The analytical method can obtain the exact solution; however, it is limited to small-sized systems while the numerical methods can approximate the solution for large dimensional systems up to <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:mn>100<\/a:mn>\n                        <a:mo>\u00d7<\/a:mo>\n                        <a:mn>100<\/a:mn>\n                     <\/a:math>\n                  <\/jats:inline-formula> with a very small error bound for any initial value. In addition, the proposed methods are applied to other fuzzy systems such as Sylvester and Lyapunov matrix equations. The proposed methods are illustrated by solving numerical examples with different size systems.<\/jats:p>","DOI":"10.1155\/2022\/8926038","type":"journal-article","created":{"date-parts":[[2022,1,27]],"date-time":"2022-01-27T17:05:42Z","timestamp":1643303142000},"page":"1-29","source":"Crossref","is-referenced-by-count":5,"title":["Numerical Solutions for Coupled Trapezoidal Fully Fuzzy Sylvester Matrix Equations"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9255-200X","authenticated-orcid":true,"given":"Ahmed AbdelAziz","family":"Elsayed","sequence":"first","affiliation":[{"name":"School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia"},{"name":"Department of Mathematics, Institute of Applied Technology, Mohamed Bin Zayed City, UAE"}]},{"given":"Nazihah","family":"Ahmad","sequence":"additional","affiliation":[{"name":"School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia"}]},{"given":"Ghassan","family":"Malkawi","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Math and Natural Science Division, Higher Colleges of Technology (HCT), Al Ain, UAE"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1109\/9.284883"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.919562"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1109\/9.751347"},{"key":"4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-0727-9","volume-title":"Control of Linear Systems with Regulation and Input Constraints","author":"A. 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