{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:18:45Z","timestamp":1760242725368,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,3,11]],"date-time":"2016-03-11T00:00:00Z","timestamp":1457654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This article proposes a novel weak fuzzy solution for the fuzzy linear system. As a matter of fact, we define the right-hand side column of the fuzzy linear system as a piecewise fuzzy function to overcome the related shortcoming, which exists in the previous findings. The strong point of this proposal is that the weak fuzzy solution is always a fuzzy number vector. Two complex and non-complex linear systems under uncertainty are tested to validate the effectiveness and correctness of the presented method.<\/jats:p>","DOI":"10.3390\/e18030068","type":"journal-article","created":{"date-parts":[[2016,3,14]],"date-time":"2016-03-14T11:03:45Z","timestamp":1457953425000},"page":"68","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Novel Weak Fuzzy Solution for Fuzzy Linear System"],"prefix":"10.3390","volume":"18","author":[{"given":"Soheil","family":"Salahshour","sequence":"first","affiliation":[{"name":"Young Researchers and Elite Club, Islamic Azad University, Mobarakeh Branch, Mobarakeh, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali","family":"Ahmadian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Universti Putra Malaysia, 43400 Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fudziah","family":"Ismail","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Universti Putra Malaysia, 43400 Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Cankaya University, 06530 Ankara, Turkey"},{"name":"Institute of Space Sciences, P.O.Box MG-23, Magurele-Bucharest RO-76911, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,3,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4494","DOI":"10.1016\/j.apm.2014.12.018","article-title":"A new Walk on Equations Monte Carlo method for solving systems of linear algebraic equations","volume":"39","author":"Dimov","year":"2015","journal-title":"Appl. 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