{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T23:51:02Z","timestamp":1770681062546,"version":"3.49.0"},"reference-count":21,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2016,7,29]],"date-time":"2016-07-29T00:00:00Z","timestamp":1469750400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2016,9]]},"abstract":"<jats:p>The occurrence of imprecision in the real world is inevitable due to some unexpected situations. The imprecision is often involved in any engineering design process. The imprecision and uncertainty are often interpreted as fuzziness. Fuzzy systems have an essential role in the uncertainty modeling, which can formulate the uncertainty in the actual environment. In this paper, a new method based on linear algebra for resolution of a fuzzy complex system of linear equations is presented. Moreover, a new algorithm is designed to find all the solutions of the system based on the eigenvalue method. Thanks to our approach, we can find all the solutions of the system at a time. Also, we are able to determine when the solution sets of the system are nonempty sets.To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed.<\/jats:p>","DOI":"10.3233\/jifs-152046","type":"journal-article","created":{"date-parts":[[2016,7,29]],"date-time":"2016-07-29T11:29:09Z","timestamp":1469791749000},"page":"1689-1699","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Solving fuzzy complex system of linear equations using eigenvalue method"],"prefix":"10.1177","volume":"31","author":[{"given":"Hamed","family":"Farahani","sequence":"first","affiliation":[{"name":"Department of Basic Science, Chabahar Maritime University, Chabahar, Iran"}]},{"given":"Hassan Mishmast","family":"Nehi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran"}]},{"given":"Mahmoud","family":"Paripour","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hamedan University of Technology, Hamedan, Iran"}]}],"member":"179","published-online":{"date-parts":[[2016,7,29]]},"reference":[{"key":"e_1_3_1_2_2","first-page":"1985","volume-title":"Gr\u00f6bner bases: An algorithmic method in polynomial ideal theory","author":"Buchberger B.","unstructured":"BuchbergerB., Gr\u00f6bner bases: An algorithmic method in polynomial ideal theory, CompanyR.P., (Ed.), Recent Trends in Multidimensional System Theory, Bose, 1985."},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11155-006-2968-5"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10598-012-9152-z"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.02.014"},{"key":"e_1_3_1_6_2","volume-title":"Using Algebraic Geometry","author":"Cox D.","year":"2004","unstructured":"CoxD., LittleJ., and O\u2019SheaD., Using Algebraic Geometry, second edition, Springer-VarlagNew York, 2004."},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-35651-8"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0888-613X(91)90013-C"},{"key":"e_1_3_1_9_2","article-title":"Theory and Applications Prentice Hall P T R","author":"Klir G.J.","year":"1995","unstructured":"KlirG.J., and YuanB., Theory and Applications Prentice Hall P T R, Fuzzy sets and fuzzy logic, 1995.","journal-title":"Fuzzy sets and fuzzy logic"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90122-X"},{"key":"e_1_3_1_11_2","first-page":"1","article-title":"A new efficient algorithm for computing Gr\u00f6bner bases (F4)","volume":"139","author":"Faug\u00e8re J.-C.","year":"1999","unstructured":"Faug\u00e8reJ.-C., A new efficient algorithm for computing Gr\u00f6bner bases (F4), em Journal of Pure and Applied Algebra139 (1999), 1\u20133, 61\u201388.","journal-title":"em Journal of Pure and Applied Algebra"},{"key":"e_1_3_1_12_2","volume-title":"A new efficient algorithm for computing Gr\u00f6bner bases without reduction to zero ( F5)","author":"Faug\u00e8re J.-C.","year":"2002","unstructured":"Faug\u00e8reJ.-C., A new efficient algorithm for computing Gr\u00f6bner bases without reduction to zero ( F5), in: MoraT. 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