{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T04:13:57Z","timestamp":1759032837303},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["New Math. and Nat. Computation"],"published-print":{"date-parts":[[2018,7]]},"abstract":"<jats:p>Fuzzy relations are fundamental in applications of fuzzy set theory and fuzzy logic. The entire literature on fuzzy relations as applied to fuzzy graph theory are based on Rosenfeld\u2019s relations. Rosenfeld used minimum and maximum as the norm and conorm in his study of compositions of fuzzy relations. In this paper, we generalize fuzzy relations using arbitrary [Formula: see text]-norms and [Formula: see text]-conorms. Many of the results do not hold when minimum and maximum are replaced by an arbitrary norm and an arbitrary conorm. Reflexive, symmetric and transitive generalized fuzzy relations are also discussed and an application to human trafficking and illegal immigration is presented.<\/jats:p>","DOI":"10.1142\/s1793005718500126","type":"journal-article","created":{"date-parts":[[2018,3,14]],"date-time":"2018-03-14T07:27:03Z","timestamp":1521012423000},"page":"187-202","source":"Crossref","is-referenced-by-count":8,"title":["Generalized Fuzzy Relations"],"prefix":"10.1142","volume":"14","author":[{"given":"John N.","family":"Mordeson","sequence":"first","affiliation":[{"name":"Department of Mathematics, Creighton University, Omaha, Nebraska 68178, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sunil","family":"Mathew","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology, Calicut, Kerala 673601, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Davender S.","family":"Malik","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Creighton University, Omaha, Nebraska 68178, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,6,3]]},"reference":[{"key":"S1793005718500126BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"S1793005718500126BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.02.012"},{"key":"S1793005718500126BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90036-5"},{"key":"S1793005718500126BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(71)80005-1"},{"key":"S1793005718500126BIB005","unstructured":"A. Kaufmann , Introduction a la Theorie des Sous Ensembles Flous, Vol. 1, Masson, Paris, (1973) 41\u2013189."},{"key":"S1793005718500126BIB006","volume-title":"Introduction to the Theory of Fuzzy Sets","volume":"1","author":"Kaufmann A.","year":"1973"},{"key":"S1793005718500126BIB007","doi-asserted-by":"crossref","unstructured":"A. Rosenfeld , Fuzzy graphs, Fuzzy Sets and Their Applications, L. A. Zadeh, K. S. Fu and M. Shimura (eds.) (Academic Press, New York, 1975), pp. 77\u201395.","DOI":"10.1016\/B978-0-12-775260-0.50008-6"},{"key":"S1793005718500126BIB008","first-page":"125","volume-title":"Fuzzy Sets and Their Applications","author":"Yeh R. T.","year":"1997"},{"key":"S1793005718500126BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1854-3"},{"key":"S1793005718500126BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1808-6"},{"key":"S1793005718500126BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90057-B"},{"key":"S1793005718500126BIB013","first-page":"1692","volume":"6","author":"Myna R.","year":"2015","journal-title":"Mathematical Journal of Scientific and Engineering Research"},{"key":"S1793005718500126BIB015","first-page":"6","volume":"1","author":"Swaminathan S.","year":"2012","journal-title":"International Journal of Engineering and Technology"},{"key":"S1793005718500126BIB016","doi-asserted-by":"publisher","DOI":"10.15807\/jorsj.19.217"},{"key":"S1793005718500126BIB017","first-page":"11","volume":"10","author":"Sun H.","year":"1997","journal-title":"Space Med Eng"},{"key":"S1793005718500126BIB018","first-page":"21","volume":"10","author":"Lytvnenko N.","year":"2015","journal-title":"Advances in Military Technology"},{"key":"S1793005718500126BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/B978-012598910-7\/50009-3"},{"key":"S1793005718500126BIB021","doi-asserted-by":"publisher","DOI":"10.1142\/S1793005717400063"},{"key":"S1793005718500126BIB022","doi-asserted-by":"publisher","DOI":"10.1142\/S1793005718500096"},{"issue":"1","key":"S1793005718500126BIB023","first-page":"147","volume":"14","author":"Mordeson N.","year":"2018","journal-title":"Advances in Fuzzy Sets and Systems"},{"key":"S1793005718500126BIB024","doi-asserted-by":"publisher","DOI":"10.1142\/S1793005718500047"}],"container-title":["New Mathematics and Natural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793005718500126","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T00:14:03Z","timestamp":1660608843000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793005718500126"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,3]]},"references-count":21,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2018,6,3]]},"published-print":{"date-parts":[[2018,7]]}},"alternative-id":["10.1142\/S1793005718500126"],"URL":"https:\/\/doi.org\/10.1142\/s1793005718500126","relation":{},"ISSN":["1793-0057","1793-7027"],"issn-type":[{"value":"1793-0057","type":"print"},{"value":"1793-7027","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,3]]}}}