{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T15:15:07Z","timestamp":1770045307813,"version":"3.49.0"},"reference-count":20,"publisher":"SAGE Publications","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,12,16]]},"abstract":"<jats:p>In this paper, we introduce new types of fuzzy (m, n)-ideals in ordered semigroups. In fact, the notion of (\u2208\u00a0, \u2208\u00a0\u2228\u00a0(\u03ba*, q\u03ba))-fuzzy (m, n)-ideals of the ordered semigroups is introduced. Further, we present the characterzations of this notion in different ways. Then the (\u03ba*, \u03ba)-lower part of the (\u2208\u00a0, \u2208\u00a0\u2228\u00a0(\u03ba*, q\u03ba))-fuzzy (m, n)-ideals is defined and its associated properties are investigated. After that, (m, n)-regular ordered semigroups are characterized in terms of its (\u2208\u00a0, \u2208\u00a0\u2228\u00a0(\u03ba*, q\u03ba))-fuzzy (m, n)-ideals and their (\u03ba*, \u03ba)-lower parts.<\/jats:p>","DOI":"10.3233\/jifs-210378","type":"journal-article","created":{"date-parts":[[2021,9,14]],"date-time":"2021-09-14T10:40:44Z","timestamp":1631616044000},"page":"6561-6574","source":"Crossref","is-referenced-by-count":6,"title":["New types of fuzzy (m, n)-ideals in ordered semigroups"],"prefix":"10.1177","volume":"41","author":[{"given":"G.","family":"Muhiuddin","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia"}]},{"given":"A.","family":"Mahboob","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle, India"}]},{"given":"N. M.","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh, India"}]},{"given":"D.","family":"Al-Kadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistic, College of Science, Taif University, Taif, Saudi Arabia"}]}],"member":"179","reference":[{"issue":"2","key":"10.3233\/JIFS-210378_ref1","first-page":"199","article-title":"On (m, n)-ideals on (m, n)-regular ordered semigroups","volume":"38","author":"Bussaban","year":"2016","journal-title":"Songklanakarin J Sci Tech"},{"issue":"3","key":"10.3233\/JIFS-210378_ref2","first-page":"391","article-title":"Ordered semigroup characterized by their (\u2208, \u2208\u00a0\u2228)-fuzzy bi-ideals","volume":"32","author":"Jun","year":"2009","journal-title":"Bull Malays Math Soc"},{"issue":"4","key":"10.3233\/JIFS-210378_ref3","first-page":"359","article-title":"A novel generalization of fuzzy subsemigroups","volume":"14","author":"Jun","year":"2017","journal-title":"Annals of Fuzzy Mathematics and Informatics"},{"issue":"3","key":"10.3233\/JIFS-210378_ref4","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.3233\/IFS-151869","article-title":"Hesitant fuzzy semigroups with a frontier","volume":"30","author":"Jun","year":"2016","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"10.3233\/JIFS-210378_ref5","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1155\/2014\/467968","article-title":"Concave Soft Sets, Critical Soft Points, and Union-Soft Ideals of Ordered Semigroups","volume":"2014","author":"Jun","year":"2014","journal-title":"The ScientificWorld Journal"},{"key":"10.3233\/JIFS-210378_ref6","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1007\/s002330010079","article-title":"Fuzzy sets in ordered groupoids","volume":"65","author":"Kehayopulu","year":"2002","journal-title":"Semigroup Forum"},{"issue":"1","key":"10.3233\/JIFS-210378_ref7","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.3233\/JIFS-16339","article-title":"Ordered semigroups characterized in terms of generalized fuzzy ideals","volume":"32","author":"Khan","year":"2017","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"suppl.","key":"10.3233\/JIFS-210378_ref8","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/s00521-011-0731-2","article-title":"Ordered semigroups characterized by (\u2208, \u2002\u00a0\u2208\u00a0\u2002\u00a0\u2228\u00a0q\u03ba)-fuzzy generalized biideals","volume":"21","author":"Khan","year":"2012","journal-title":"Neural Comput and Applic"},{"issue":"6","key":"10.3233\/JIFS-210378_ref9","first-page":"835","article-title":"Fuzzy fiters of ordered semigroups","volume":"12","author":"Khan","year":"2016","journal-title":"Annals of Fuzzy Mathematics and Informatics"},{"key":"10.3233\/JIFS-210378_ref10","first-page":"17","article-title":"Fuzzy bi-ideals in semigroups","volume":"28","author":"Kuroki","year":"1979","journal-title":"Comment Math Univ St Pauli"},{"key":"10.3233\/JIFS-210378_ref11","doi-asserted-by":"crossref","first-page":"401","DOI":"10.3390\/math7050401","article-title":"Characterizations of Regular Ordered Semigroups by (\u2208, \u2002\u00a0\u2208\u00a0\u2002\u00a0\u2228\u00a0(\u03ba*, q\u03ba))-Fuzzy Quasi-Ideals","volume":"7","author":"Mahboob","year":"2019","journal-title":"Mathematics"},{"issue":"3","key":"10.3233\/JIFS-210378_ref12","doi-asserted-by":"crossref","first-page":"4195","DOI":"10.3233\/JIFS-190293","article-title":"A new type of fuzzy semiprime subsets in ordered semigroups","volume":"37","author":"Muhiuddin","year":"2019","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"3","key":"10.3233\/JIFS-210378_ref13","doi-asserted-by":"crossref","first-page":"2412","DOI":"10.3934\/math.2020159","article-title":"Int-soft ideals over the soft sets in ordered semigroups","volume":"5","author":"Muhiuddin","year":"2020","journal-title":"AIMS Mathematics"},{"issue":"1","key":"10.3233\/JIFS-210378_ref14","first-page":"463","article-title":"Cubic interior ideals in semigroups","volume":"14","author":"Muhiuddin","year":"2019","journal-title":"Applications and Applied Mathematics"},{"issue":"2","key":"10.3233\/JIFS-210378_ref15","first-page":"73","article-title":"A generalization of (\u2208, \u2208\u00a0\u2228\u00a0q)\u2013fuzzy ideals in ternary semigroups","volume":"2","author":"Muhiuddin","year":"2019","journal-title":"Annals of Communications in Mathematics"},{"key":"10.3233\/JIFS-210378_ref16","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1155\/2020\/8856287","article-title":"Generalized hesitant fuzzy ideals in semigroups","volume":"2020","author":"Muhiuddin","year":"2020","journal-title":"Journal of Mathematics"},{"issue":"1","key":"10.3233\/JIFS-210378_ref17","first-page":"1","article-title":"Neutrosophic Subsemigroups","volume":"1","author":"Muhiuddin","year":"2018","journal-title":"Annals of Communications in Mathematics"},{"key":"10.3233\/JIFS-210378_ref18","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1016\/0022-247X(71)90199-5","article-title":"Fuzzy subgroups","volume":"35","author":"Rosenfeld","year":"1971","journal-title":"J Math Anal Appl"},{"key":"10.3233\/JIFS-210378_ref19","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/j.camwa.2009.06.014","article-title":"Characterizations of regular semigroups by (\u2208, \u2002\u00a0\u2208\u00a0\u2002\u00a0\u2228\u00a0q\u03ba)-fuzzy ideals","volume":"59","author":"Shabir","year":"2010","journal-title":"Comput Math Appl"},{"issue":"1965","key":"10.3233\/JIFS-210378_ref20","first-page":"338","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","journal-title":"Information and Control"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-210378","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T03:24:58Z","timestamp":1770002698000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-210378"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,16]]},"references-count":20,"journal-issue":{"issue":"6"},"URL":"https:\/\/doi.org\/10.3233\/jifs-210378","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,16]]}}}