{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:32:58Z","timestamp":1777703578757,"version":"3.51.4"},"reference-count":34,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2017,2,24]],"date-time":"2017-02-24T00:00:00Z","timestamp":1487894400000},"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":[[2017,2,24]]},"abstract":"\n The main motivation behind this paper is to study some structural properties of a non-associative structure (\n \n LA<\/mml:mi>\n <\/mml:math>\n -semigroup) in terms of fuzzy sets as it hasn\u2019t attracted much attention compared to associative structures. An\n \n LA<\/mml:mi>\n <\/mml:math>\n -semigroup can be referred to as a non-associative semigroup, as the main difference between a semigroup and an\n \n LA<\/mml:mi>\n <\/mml:math>\n -semigroup is the switching of an associative law. In this paper, we introduce and characterize fuzzy (0, 2)-ideals, fuzzy (0, 2)-bi-ideals and fuzzy (1, 2)-ideals of an\n \n LA<\/mml:mi>\n <\/mml:math>\n -semigroup. We give a new and alternate definition for a strongly regular element of a unitary\n \n LA<\/mml:mi>\n <\/mml:math>\n -semigroup and show novel conditions under which a strongly regular\n \n LA<\/mml:mi>\n <\/mml:math>\n -semigroup becomes an\n \n \n LA<\/mml:mi>\n \n \n *<\/mml:mo>\n *<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n -semigroup. These characterizations do not exist in literature before this work. As an application of our results we get characterizations of a strongly regular\n \n LA<\/mml:mi>\n <\/mml:math>\n -semigroup in terms of fuzzy one-sided ideals and fuzzy bi-ideals. Finally we introduce and investigate the properties of fuzzy inner-unitary\n \n LA<\/mml:mi>\n <\/mml:math>\n -subsemigroups in an\n \n \n LA<\/mml:mi>\n \n \n *<\/mml:mo>\n *<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n -semigroup. These concepts will help in verifying the existing characterizations and will help in achieving new and generalized results in future works.\n <\/jats:p>","DOI":"10.3233\/jifs-161299","type":"journal-article","created":{"date-parts":[[2017,2,28]],"date-time":"2017-02-28T11:20:14Z","timestamp":1488280814000},"page":"1917-1930","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Some studies in fuzzy non-associative semigroups"],"prefix":"10.1177","volume":"32","author":[{"given":"Faisal","family":"Yousafzai","sequence":"first","affiliation":[{"name":"Military College of Engineering, National University of Sciences and Technology, Islamabad, Pakistan"}]},{"given":"Mohammed M.","family":"Khalaf","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia"},{"name":"Higher Institute of Engineering and Technology, King Mariout, Egypt"}]},{"given":"Murad-ul-Islam","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of IT, Haripur University, Haripur, K.P.K., Pakistan"}]},{"given":"A.","family":"Borumand Saeid","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran"}]},{"given":"Quaid","family":"Iqbal","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Science and Technology of China, Hefei, China"}]}],"member":"179","published-online":{"date-parts":[[2017,2,24]]},"reference":[{"key":"e_1_3_2_2_2","first-page":"203","article-title":"Congruences on completely inverse AG**-groupoids","volume":"20","author":"Dudek W.A.","year":"2012","unstructured":"DudekW.A. and GigonR.S., Congruences on completely inverse AG**-groupoids, Quasigroups and Related Systems 20 (2012), 203\u2013209.","journal-title":"Quasigroups and Related Systems"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-013-9465-z"},{"key":"e_1_3_2_4_2","first-page":"1","article-title":"Quasi and otherwise","volume":"7","author":"Frank T.S.","year":"1965","unstructured":"FrankT.S., Quasi and otherwise, Amar Math Monthly 7 (1965), 1\u20137.","journal-title":"Amar Math Monthly"},{"issue":"3","key":"e_1_3_2_5_2","first-page":"93","article-title":"A note on Hv-LAsemigroups","volume":"77","author":"Gulistan M.","year":"2015","unstructured":"GulistanM., YaqoobN. and ShahzadM., A note on Hv-LAsemigroups, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics 77(3) (2015), 93\u2013106.","journal-title":"UPB Scientific Bulletin, Series A: Applied Mathematics and Physics"},{"issue":"2","key":"e_1_3_2_6_2","first-page":"767","article-title":"Direct product of generalized cubic sets in Hv-LA-semigroups","volume":"28","author":"Gulistan M.","year":"2016","unstructured":"GulistanM., KhanM., YaqoobN., ShahzadM. and AshrafU., Direct product of generalized cubic sets in Hv-LA-semigroups, Science International (Lahore) 28(2) (2016), 767\u2013779.","journal-title":"Science International (Lahore)"},{"key":"e_1_3_2_7_2","unstructured":"KamranM.S. 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