{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T12:31:15Z","timestamp":1770553875453,"version":"3.49.0"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["New Math. and Nat. Computation"],"published-print":{"date-parts":[[2024,7]]},"abstract":"<jats:p> The foundation of Gr\u00f6bner\u2019s work is a potent approach for separating polynomial systems of equations. In this study, we solve complex fuzzy systems of linear equations utilizing Gr\u00f6bner\u2019s basic technique. First, a system of explicit polynomial equations is generated by applying fuzzy computations and fuzzy complex computations to the fundamental system. Taking into account the lexicographical order, Gr\u00f6bner\u2019s basis is then determined for the ideal given by a definite equivalent polynomial system. The Gr\u00f6bnerbase that was obtained has a high triangular structure. Thus, the system solution may be readily implemented by proceeding. Hence, all of the system\u2019s answers are readily attainable. Next, a criterion is established to identify whether or not a solution exists for the primary system. The advantage of the proposed approach is that it acquires all of the problem\u2019s solutions simultaneously. Using this technique, a mathematical example and an application issue based on an electrical circuit are resolved. Comparing the generated findings to the known outcomes reveals a high level of congruence. <\/jats:p>","DOI":"10.1142\/s1793005724500297","type":"journal-article","created":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T14:29:28Z","timestamp":1687530568000},"page":"533-550","source":"Crossref","is-referenced-by-count":3,"title":["Gr\u00f6bner Basis Approach for Solving Fuzzy Complex System of Linear Equations"],"prefix":"10.1142","volume":"20","author":[{"given":"Maryam Farahmand","family":"Nejad","sequence":"first","affiliation":[{"name":"Department of Mathematics, South Tehran Branch Islamic Azad University, Tehran, Iran"}]},{"given":"Hamed","family":"Farahani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Chabahar Maritime University, Chabahar, Iran"}]},{"given":"Rahele","family":"Nuraei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, South Tehran Branch Islamic Azad University, Tehran, Iran"}]},{"given":"Alireza","family":"Gilani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, South Tehran Branch Islamic Azad University, Tehran, Iran"}]}],"member":"219","published-online":{"date-parts":[[2023,7,28]]},"reference":[{"key":"S1793005724500297BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-5225-6_6"},{"key":"S1793005724500297BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s11155-006-2968-5"},{"key":"S1793005724500297BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s10598-012-9152-z"},{"key":"S1793005724500297BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.02.014"},{"key":"S1793005724500297BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-35651-8"},{"key":"S1793005724500297BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0888-613X(91)90013-C"},{"key":"S1793005724500297BIB007","volume-title":"Fuzzy Sets and Fuzzy Logic, Theory and Applications","author":"Klir G. J.","year":"1995"},{"key":"S1793005724500297BIB008","first-page":"135","volume":"12","author":"Farahani H.","year":"2020","journal-title":"International Journal of Industrial Mathematics"},{"key":"S1793005724500297BIB009","first-page":"1689","volume":"31","author":"Farahani H.","year":"2016","journal-title":"Soft Computing"},{"key":"S1793005724500297BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90122-X"},{"key":"S1793005724500297BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(99)00005-5"},{"key":"S1793005724500297BIB012","first-page":"75","volume-title":"Proceedings of ISSAC","author":"Faug\u00e8re J.-C.","year":"2000"},{"key":"S1793005724500297BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00160-2"},{"key":"S1793005724500297BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(99)00076-7"},{"key":"S1793005724500297BIB015","doi-asserted-by":"publisher","DOI":"10.1145\/362515.362563"},{"key":"S1793005724500297BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90036-5"},{"key":"S1793005724500297BIB017","first-page":"78","volume":"14","author":"Hladik M. K.","year":"2010","journal-title":"Reliable Computing"},{"key":"S1793005724500297BIB018","first-page":"21","volume":"2","author":"Jahantigh M. A.","year":"2010","journal-title":"International Journal of Industrial Mathematics"},{"key":"S1793005724500297BIB019","volume-title":"Complex Interval Arithmetic and its Applications","author":"Petkovic M. S.","year":"1998"},{"key":"S1793005724500297BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(97)00010-1"},{"key":"S1793005724500297BIB021","doi-asserted-by":"publisher","DOI":"10.1145\/1837934.1837944"},{"key":"S1793005724500297BIB022","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/2969"},{"key":"S1793005724500297BIB023","volume-title":"Gr\u00f6bnerBases","author":"Becker T.","year":"1993"},{"key":"S1793005724500297BIB024","first-page":"1793","volume":"1","author":"Rahgooy T.","year":"2009","journal-title":"International Journal of Computer and Electrical Engineering"},{"key":"S1793005724500297BIB025","doi-asserted-by":"publisher","DOI":"10.1007\/s11155-006-2966-7"}],"container-title":["New Mathematics and Natural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793005724500297","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T07:43:30Z","timestamp":1722843810000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793005724500297"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,28]]},"references-count":25,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2024,7]]}},"alternative-id":["10.1142\/S1793005724500297"],"URL":"https:\/\/doi.org\/10.1142\/s1793005724500297","relation":{},"ISSN":["1793-0057","1793-7027"],"issn-type":[{"value":"1793-0057","type":"print"},{"value":"1793-7027","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,28]]}}}