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Finally, we prove that the class of symmetrical associative complete distributive extended implicative groupoids, coincides with complete residuated lattices.<\/jats:p>","DOI":"10.3233\/jifs-201575","type":"journal-article","created":{"date-parts":[[2020,11,27]],"date-time":"2020-11-27T11:08:06Z","timestamp":1606475286000},"page":"1261-1275","source":"Crossref","is-referenced-by-count":1,"title":["Extended implicative groupoids"],"prefix":"10.1177","volume":"40","author":[{"given":"E.","family":"Sameri","sequence":"first","affiliation":[{"name":"Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.A.","family":"Borzooei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-201575_ref1","doi-asserted-by":"crossref","first-page":"5471","DOI":"10.3233\/JIFS-190565","article-title":"On co-annihilators in hoops","volume":"37","author":"Aaly Kologani","year":"2019","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"4","key":"10.3233\/JIFS-201575_ref2","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1142\/S0218196703001511","article-title":"The structure of residuated lattices","volume":"13","author":"Blount","year":"2003","journal-title":"International Journal of Algebra and Computation"},{"issue":"1","key":"10.3233\/JIFS-201575_ref3","doi-asserted-by":"crossref","first-page":"139","DOI":"10.29252\/CGASA.9.1.139","article-title":"Convex L-lattice subgroups in L-ordered groups","volume":"9","author":"Borzooei","year":"2018","journal-title":"Categories and General Algebraic Structures with Applications"},{"key":"10.3233\/JIFS-201575_ref4","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.3233\/IFS-151856","article-title":"(Totally) L-ordered groups","volume":"30","author":"Borzooei","year":"2016","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"10.3233\/JIFS-201575_ref5","doi-asserted-by":"crossref","first-page":"157","DOI":"10.3233\/IFS-141286","article-title":"The category of soft sets","volume":"28","author":"Borzooei","year":"2015","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"10.3233\/JIFS-201575_ref6","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s00500-017-2788-z","article-title":"Some connections between BCK-algebras and n-ary block codes","volume":"22","author":"Borumand Saeid","year":"2018","journal-title":"Soft Computing"},{"issue":"2","key":"10.3233\/JIFS-201575_ref8","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s11083-012-9250-8","article-title":"Associativity, commutativity and symmetry in residuated structures","volume":"30","author":"Della Stella","year":"2013","journal-title":"Order"},{"key":"10.3233\/JIFS-201575_ref9","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1007\/s00521-019-04676-x","article-title":"Wajsberg algebras of order n\u00a0(n\u00a0\u2264\u00a09)","volume":"32","author":"Flaut","year":"2020","journal-title":"Neural Computing and Applications"},{"key":"10.3233\/JIFS-201575_ref12","doi-asserted-by":"crossref","first-page":"1883","DOI":"10.1007\/s00500-012-0840-6","article-title":"Extended-order algebras and fuzzy implicators","volume":"16","author":"Guido","year":"2012","journal-title":"Soft Computing"},{"key":"10.3233\/JIFS-201575_ref13","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1016\/j.jal.2008.01.001","article-title":"Extended-order algebras","volume":"6","author":"Guido","year":"2008","journal-title":"Journal of Applied Logic"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-201575","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:42:19Z","timestamp":1777455739000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-201575"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,4]]},"references-count":10,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.3233\/jifs-201575","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,4]]}}}