{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:05:05Z","timestamp":1777705505187,"version":"3.51.4"},"reference-count":15,"publisher":"SAGE Publications","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2024,3,5]]},"abstract":"<jats:p>Rosenfeld defined a fuzzy subgroup of a given group as a fuzzy subset with two special conditions and Mustafa Demirci proposed the idea of fuzzifying the operations on a group through a fuzzy equality and a fuzzy equivalence relation. This paper mainly focuses on fuzzy subsets and vague sets of monoids with several extended algebraic properties. Firstly, we generalize some algebraic properties of t-norms to fuzzy t-norms, this allows for a broader analysis and classification of fuzzy t-norms, enabling their wider application. Furthermore, we explore specific research on the properties of vague t-norms. Finally, selected conclusions about fuzzy t-norms are extended to bounded lattices.<\/jats:p>","DOI":"10.3233\/jifs-231401","type":"journal-article","created":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T11:44:22Z","timestamp":1706615062000},"page":"6881-6891","source":"Crossref","is-referenced-by-count":1,"title":["An extension of several properties for fuzzy t-norm and vague t-norm"],"prefix":"10.1177","volume":"46","author":[{"given":"Haohao","family":"Wang","sequence":"first","affiliation":[{"name":"College of Science, Northwest A&F University, Yangling, PR China"}]},{"given":"Wei","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science, Northwest A&F University, Yangling, PR China"}]},{"given":"Bin","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Science, Northwest A&F University, Yangling, PR China"}]}],"member":"179","reference":[{"issue":"3","key":"10.3233\/JIFS-231401_ref1","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1016\/0022-247X(71)90199-5","article-title":"Fuzzy groups","volume":"35","author":"Rosenfeld","year":"1971","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"1-2","key":"10.3233\/JIFS-231401_ref2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0020-0255(94)90064-7","article-title":"The lattices of fuzzy subgroups and fuzzy normal subgroups[J]","volume":"76","author":"Ajmal","year":"1994","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-231401_ref5","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.fss.2017.10.006","article-title":"Fuzzy actions","volume":"339","author":"Boixader","year":"2018","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-231401_ref8","first-page":"1120","volume":"2","author":"Zimmermann","year":"1996","journal-title":"Fuzzy Set and Its Applications"},{"issue":"04","key":"10.3233\/JIFS-231401_ref9","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1142\/S0218488597000312","article-title":"Structure of Uninorms, International Journal of Uncertainty","volume":"5","author":"Fodor","year":"1997","journal-title":"Fuzziness and Knowledge-Based Systems"},{"issue":"1","key":"10.3233\/JIFS-231401_ref10","first-page":"27","article-title":"On vague groups","volume":"5","author":"Khan","year":"2007","journal-title":"International Journal of Computational Cognition"},{"issue":"3","key":"10.3233\/JIFS-231401_ref11","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Information and Control"},{"key":"10.3233\/JIFS-231401_ref12","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/0022-247X(88)90367-8","article-title":"Some properties of fuzzy groups","volume":"133","author":"Akgul","year":"1988","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"2","key":"10.3233\/JIFS-231401_ref13","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0165-0114(97)00280-7","article-title":"Fuzzy functions and their fundamental properties","volume":"106","author":"Demirci","year":"1999","journal-title":"Fuzzy Sets and Systems"},{"issue":"1","key":"10.3233\/JIFS-231401_ref14","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1006\/jmaa.1998.6182","article-title":"Vague Groups","volume":"230","author":"Demirci","year":"1999","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"2","key":"10.3233\/JIFS-231401_ref15","first-page":"10","article-title":"Vague normal groups","volume":"6","author":"Ramakrishna","year":"2008","journal-title":"International Journal of Computational Cognition"},{"issue":"1","key":"10.3233\/JIFS-231401_ref16","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/0022-247X(81)90164-5","article-title":"Fuzzy groups and level subgroups","volume":"84","author":"Das","year":"1981","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"10.3233\/JIFS-231401_ref17","first-page":"1","article-title":"t-norms over q-fuzzy subgroups of group","volume":"12","author":"Rasuli","year":"2019","journal-title":"Jordan Journal of Mathematics and Statistics (JJMS)"},{"key":"10.3233\/JIFS-231401_ref19","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/S0165-0114(99)00125-6","article-title":"The functional equations of Frank and Alsina for uninorms and nullnorms","volume":"120","author":"Calvo","year":"2001","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-231401_ref20","doi-asserted-by":"crossref","first-page":"1762","DOI":"10.1109\/TFUZZ.2021.3066120","article-title":"Ordinal sum of two binary operations being a t-norm on bounded lattice","volume":"30","author":"Wu","year":"2020","journal-title":"IEEE Transactions on Fuzzy Systems"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-231401","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:44:03Z","timestamp":1777455843000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-231401"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,5]]},"references-count":15,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.3233\/jifs-231401","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,5]]}}}