{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T18:15:32Z","timestamp":1769710532932,"version":"3.49.0"},"reference-count":25,"publisher":"SAGE Publications","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,5,4]]},"abstract":"<jats:p>\u00a0In paper the generalized real eigenvalue and fuzzy eigenvector of a crisp real symmetric matrix with respect to another real symmetric matrix is studied. The original generalized fuzzy eigen problem is extended into a crisp generalized eigen problem of a real symmetric matrix with high orders using the arithmetic operation of LR fuzzy matrix and vector. Two cases are analysed: (a) the unknown eigenvalue \u03bb is a non negative real number; (b) the unknown eigenvalue \u03bb is a negative real number. Two computing models are established and an algorithm for finding the generalized fuzzy eigenvector of a real symmetric matrix is derived. Moreover, a sufficient condition for the existence of a strong generalized fuzzy eigenvector is given. Some numerical examples are shown to illustrated our proposed method.<\/jats:p>","DOI":"10.3233\/jifs-222641","type":"journal-article","created":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T11:43:09Z","timestamp":1676029389000},"page":"7459-7467","source":"Crossref","is-referenced-by-count":3,"title":["Generalized fuzzy eigenvectors of real symmetric matrices1"],"prefix":"10.1177","volume":"44","author":[{"given":"Xiaobin","family":"Guo","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, China"}]},{"given":"Ying","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, China"}]},{"given":"Quanxiu","family":"Zhuo","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, China"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-222641_ref1","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/S0096-3003(03)00793-8","article-title":"Numerical methods for fuzzy system of linear equations","volume":"153","author":"Allahviranloo","year":"2004","journal-title":"Applied Mathematics and Computation"},{"key":"10.3233\/JIFS-222641_ref2","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/s00500-011-0739-7","article-title":"A new approach to obtain algebraic solution of interval linear systems","volume":"16","author":"Allahviranloo","year":"2012","journal-title":"Soft Computing"},{"key":"10.3233\/JIFS-222641_ref3","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.fss.2011.02.010","article-title":"A note on \u201cFuzzy linear systems\u201d","volume":"177","author":"Allahviranloo","year":"2011","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-222641_ref4","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1007\/s00521-012-1062-7","article-title":"A method to find fuzzy eigenvalues and fuzzy eigenvectors of fuzzy matrix","volume":"23","author":"Allahviranloo","year":"2013","journal-title":"Neural Comput and Applic"},{"key":"10.3233\/JIFS-222641_ref5","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1016\/j.apm.2012.03.037","article-title":"On the fuzzy solution of LR fuzzy linear systems","volume":"37","author":"Allahviranloo","year":"2013","journal-title":"Applied Mathematical Modelling"},{"key":"10.3233\/JIFS-222641_ref6","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/0165-0114(90)90158-3","article-title":"Fuzzy eigenvalue problems and input output analysis","volume":"34","author":"Buckley","year":"1998","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-222641_ref7","first-page":"31","article-title":"Generalized fuzzy eigenvalue problems","volume":"14","author":"Chiao","year":"1998","journal-title":"Tamsui Oxf J Math Sci"},{"key":"10.3233\/JIFS-222641_ref9","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S0165-0114(96)00270-9","article-title":"Fuzzy linear systems","volume":"96","author":"Friedman","year":"1998","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-222641_ref10","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/0165-0114(86)90026-6","article-title":"Elementary calculus","volume":"18","author":"Goetschel","year":"1986","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-222641_ref11","doi-asserted-by":"crossref","first-page":"1456","DOI":"10.1016\/j.apm.2010.09.022","article-title":"Inconsistent fuzzy matrix equations and its fuzzy least squares solutions","volume":"35","author":"Gong","year":"2011","journal-title":"Applied Mathematical Modelling"},{"key":"10.3233\/JIFS-222641_ref12","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.ins.2013.12.054","article-title":"Approximate solution of dual fuzzy matrix equations","volume":"266","author":"Gong","year":"2014","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-222641_ref13","first-page":"33","article-title":"Solving LR fuzzy linear matrix equation","volume":"16","author":"Guo","year":"2019","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"10.3233\/JIFS-222641_ref15","doi-asserted-by":"crossref","first-page":"2617","DOI":"10.3233\/JIFS-17072","article-title":"Further investigation to dual fuzzy matrix equation","volume":"33","author":"Guo","year":"2017","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"10.3233\/JIFS-222641_ref16","unstructured":"Maolin Hu, Matrix computation and its applications, Beijing: Science press,, 1 (2008). 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