{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T13:58:52Z","timestamp":1770818332482,"version":"3.50.1"},"reference-count":0,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"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":[[2014,4]]},"abstract":"<jats:p>The aim of this paper is further to develop the fuzzy filter theory and fuzzy congruence relation on a residuated lattice. First, we introduce the concepts of interval-valued $\\mathcal{T}$-fuzzy (implicative, positive implicative, MV, regular) filters with respect to a t-norm $\\mathcal{T}$ on D[0,1] and investigate their properties, and some equivalent characterizations of these generalized fuzzy filters are derived. Next, we introduce the concept of interval-valued $\\mathcal{T}$-fuzzy congruence relation on a residuated lattice, and the relation between interval-valued $\\mathcal{T}$-fuzzy congruences and interval-valued $\\mathcal{T}$-fuzzy filters are investigated. Finally, we construct a new residuated lattice which induced by interval-valued $\\mathcal{T}$-fuzzy congruences, the homomorphism theorem is given.<\/jats:p>","DOI":"10.3233\/ifs-130879","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T18:27:50Z","timestamp":1575311270000},"page":"2021-2033","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["Interval-valued $\\mathcal{T}$-fuzzy filters and interval-valued $\\mathcal{T}$-fuzzy congruences on residuated lattices"],"prefix":"10.1177","volume":"26","author":[{"given":"Yi","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan province, P.R. China"},{"name":"Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, Sichuan province, P.R. China"}]},{"given":"Yang","family":"Xu","sequence":"additional","affiliation":[{"name":"Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, Sichuan province, P.R. China"}]},{"given":"Xiaoyan","family":"Qin","sequence":"additional","affiliation":[{"name":"Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, Sichuan province, P.R. China"}]}],"member":"179","published-online":{"date-parts":[[2014,1]]},"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-130879","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-130879","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T12:27:18Z","timestamp":1770812838000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/IFS-130879"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,4]]}},"alternative-id":["10.3233\/IFS-130879"],"URL":"https:\/\/doi.org\/10.3233\/ifs-130879","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}