{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:37:13Z","timestamp":1753886233405,"version":"3.41.2"},"reference-count":23,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2009,8,30]],"date-time":"2009-08-30T00:00:00Z","timestamp":1251590400000},"content-version":"vor","delay-in-days":241,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>We establish, by means of a large class of\ncontinuous t\u2010representable intuitionistic fuzzy t\u2010conorms, a factorization of an intuitionistic fuzzy relation (IFR) into a\nunique indifference component and a family of regular strict components. This result generalizes a previous factorization\nobtained by Dimitrov (2002) with the (max\u2009, min\u2009)\nintuitionistic fuzzy t\u2010conorm. We provide, for a  continuous\nt\u2010representable intuitionistic fuzzy t\u2010norm <jats:italic>\ud835\udcaf<\/jats:italic>, a characterization of the <jats:italic>\ud835\udcaf<\/jats:italic>\u2010transitivity of an IFR. This enables us to determine necessary and sufficient conditions on a\n<jats:italic>\ud835\udcaf<\/jats:italic>\u2010transitive IFR <jats:italic>R<\/jats:italic> under which a strict component of\n<jats:italic>R<\/jats:italic> satisfies pos\u2010transitivity and negative transitivity.<\/jats:p>","DOI":"10.1155\/2009\/580918","type":"journal-article","created":{"date-parts":[[2009,8,30]],"date-time":"2009-08-30T13:00:17Z","timestamp":1251637217000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components"],"prefix":"10.1155","volume":"2009","author":[{"given":"Louis Aim\u00e9","family":"Fono","sequence":"first","affiliation":[]},{"given":"Gilbert","family":"Njanpong Nana","sequence":"additional","affiliation":[]},{"given":"Maurice","family":"Salles","sequence":"additional","affiliation":[]},{"given":"Henri","family":"Gwet","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,8,30]]},"reference":[{"key":"e_1_2_9_1_2","first-page":"338","article-title":"Fuzzy sets","volume":"8","author":"Zadeh L. 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