{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:45:22Z","timestamp":1777704322643,"version":"3.51.4"},"reference-count":20,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2018,8,10]],"date-time":"2018-08-10T00:00:00Z","timestamp":1533859200000},"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 & Fuzzy Systems"],"published-print":{"date-parts":[[2018,10]]},"abstract":"\n We give the notion of fuzzy congruences in a\n non-associative semigroup<\/jats:italic>\n briefly known as Abel-Grassmann\u2019s groupoid. First, we study fuzzy full, fuzzy self-conjugate, fuzzy normal subgroupoids and show that fuzzy kernel\n \u03ba<\/jats:italic>\n and fuzzy trace\n \u03c4<\/jats:italic>\n of a congruence make up a congruence pair (\n \u03ba<\/jats:italic>\n ,\n \u03c4<\/jats:italic>\n )\u00a0. Then, we investigate fuzzy idempotent-separating congruence and show that\n \u03bc<\/jats:italic>\n \n (\n \u03ba<\/jats:italic>\n ,\n \u03c4<\/jats:italic>\n )\n <\/jats:sub>\n is a unique fuzzy congruence. Next, we study the lattice of fuzzy congruences, fuzzy congruence relations\n \u03c6<\/jats:italic>\n min<\/jats:sub>\n and\n \u03c6<\/jats:italic>\n max<\/jats:sub>\n and show a relation between fuzzy kernel and fuzzy trace of\n \u03c1<\/jats:italic>\n max<\/jats:sub>\n in a completely inverse AG\n **<\/jats:sup>\n -groupoid.\n <\/jats:p>","DOI":"10.3233\/jifs-18663","type":"journal-article","created":{"date-parts":[[2018,8,14]],"date-time":"2018-08-14T15:56:51Z","timestamp":1534262211000},"page":"3783-3796","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Fuzzy congruences on non-associative semigroups"],"prefix":"10.1177","volume":"35","author":[{"given":"Waqar","family":"Khan","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beibei, Chongqing, PR China"}]},{"given":"GuiYun","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beibei, Chongqing, PR China"}]},{"given":"Bijan","family":"Davvaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yazd University, Yazd, Iran"}]}],"member":"179","published-online":{"date-parts":[[2018,8,10]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(85)90057-X"},{"key":"e_1_3_2_3_2","first-page":"1","article-title":"Kernel normal system of inverse AG**-groupoids","volume":"17","author":"Bozinovic M.","year":"2008","unstructured":"BozinovicM., ProticP. and StevanovicN., Kernel normal system of inverse AG**-groupoids, Quasigroups and Related Systems 17 (2008), 1\u20138.","journal-title":"Quasigroups and Related Systems"},{"key":"e_1_3_2_4_2","first-page":"203","article-title":"Congruences on completely inverse AG**-groupoids","volume":"20","author":"Dudek W.A.","year":"2012","unstructured":"DudekW.A. and GigonR.S., Congruences on completely inverse AG**-groupoids, Quasigroups and Related Systems 20 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abel-grassmanns groupoids, Advances in Fuzzy Mathematics 5(3) (2010), 349\u2013360.","journal-title":"Advances in Fuzzy Mathematics"},{"key":"e_1_3_2_10_2","first-page":"822","article-title":"Sandwich sets and congruences in completely inverse AG**-groupoid","volume":"39","author":"Khan W.","year":"2018","unstructured":"KhanW., HilaK. and ChenG., Sandwich sets and congruences in completely inverse AG**-groupoid, Italian Journal of Pure and Applied Mathematics 39 (2018), 822\u2013838.","journal-title":"Italian Journal of Pure and Applied Mathematics"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(92)90013-X"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-37125-0"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90077-8"},{"key":"e_1_3_2_14_2","first-page":"115","article-title":"Decomposition of a locally associative AG**-groupoid","volume":"1","author":"Mushtaq 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