{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:45:15Z","timestamp":1777704315996,"version":"3.51.4"},"reference-count":13,"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 In this paper, we introduce the notion of fuzzy filters on equality algebras and study a fuzzy filter generated by a fuzzy set. We also solve the open problem which was presented by Kadji, Lele and Tonga in [Soft Computing, 21 (2017) 1913-1922]. In addition, we denote the set of all cosets of a fuzzy filter\n f<\/jats:italic>\n by\n E<\/jats:italic>\n \/\n f<\/jats:italic>\n , and prove that the structure (\n E<\/jats:italic>\n \/\n f<\/jats:italic>\n , \u2227\u00a0, \u223c\u00a0,\n f<\/jats:italic>\n 1<\/jats:sub>\n ) is an equality algebra, and is isomorphic to the (\n E<\/jats:italic>\n \/\n f<\/jats:italic>\n \n f<\/jats:italic>\n (1)\n <\/jats:sub>\n , \u2227\u00a0, \u223c\u00a0,\n f<\/jats:italic>\n \n f<\/jats:italic>\n (1)\n <\/jats:sub>\n ), where\n f<\/jats:italic>\n \n f<\/jats:italic>\n (1)\n <\/jats:sub>\n \u00a0=\u00a0{\n x<\/jats:italic>\n \u00a0\u2208\u00a0\n E<\/jats:italic>\n |\n f<\/jats:italic>\n \u00a0(\n x<\/jats:italic>\n )\u00a0=\u00a0\n f<\/jats:italic>\n \u00a0(1)}. At the meantime, we define fuzzy congruences on equality algebras and show that there is one-to-one correspondence between fuzzy filters and fuzzy congruences. Finally, we investigate some topological properties of uniform topology induced by the special family of extreme fuzzy filters.\n <\/jats:p>","DOI":"10.3233\/jifs-18509","type":"journal-article","created":{"date-parts":[[2018,8,10]],"date-time":"2018-08-10T10:48:43Z","timestamp":1533898123000},"page":"3709-3719","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Fuzzy filters on equality algebras with applications"],"prefix":"10.1177","volume":"35","author":[{"given":"Xiao Ye","family":"Yu","sequence":"first","affiliation":[{"name":"School of Mathematics, Northwest University, Xi\u2019an, P.R. China"}]},{"given":"Xiao Long","family":"Xin","sequence":"additional","affiliation":[{"name":"School of Mathematics, Northwest University, Xi\u2019an, P.R. China"}]},{"given":"Jun Tao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Northwest University, Xi\u2019an, P.R. 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