{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:33:50Z","timestamp":1777703630728,"version":"3.51.4"},"reference-count":8,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2015,8,31]],"date-time":"2015-08-31T00:00:00Z","timestamp":1440979200000},"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 &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2015,8,31]]},"abstract":"<jats:p>\n                    In this study, using Yuan and Lee\u2019s definition of fuzzy group based on fuzzy binary operation and Aktas and Cagman definition of fuzzy ring, we give a new kind of definition to (\n                    <jats:italic>A<\/jats:italic>\n                    \u00a0:\u00a0\n                    <jats:italic>B<\/jats:italic>\n                    ). The concept of fuzzy regular and fuzzy left strongly regular are introduced and we create a new study on their basic properties equivalent to those of ordinary rings. We have shown that if (\n                    <jats:italic>R<\/jats:italic>\n                    ,\n                    <jats:italic>G<\/jats:italic>\n                    ,\n                    <jats:italic>H<\/jats:italic>\n                    ) is strongly regular, then for any\n                    <jats:italic>a<\/jats:italic>\n                    \u00a0\u2208\u00a0\n                    <jats:italic>R<\/jats:italic>\n                    ,  left annihilator of \u201c\n                    <jats:italic>a<\/jats:italic>\n                    \u201d is an ideal.\n                  <\/jats:p>","DOI":"10.3233\/ifs-151767","type":"journal-article","created":{"date-parts":[[2016,1,15]],"date-time":"2016-01-15T12:25:55Z","timestamp":1452860755000},"page":"437-442","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["A type of strongly regular rings"],"prefix":"10.1177","volume":"30","author":[{"given":"B.","family":"Sambathkumar","sequence":"first","affiliation":[{"name":"Research and Development Centre, Bharathiar University, Coimbatore, India"}]},{"given":"P.","family":"Nandakumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Perunthalaivar Kamarajar Institute of Engineering and Technology, Karaikal, India"}]},{"given":"P.","family":"Dheena","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Annamalai University, Annamalainagar, India"}]}],"member":"179","published-online":{"date-parts":[[2015,10,8]]},"reference":[{"key":"e_1_3_1_2_2","first-page":"23","article-title":"Successive sums in smooth groups and smooth cyclic group","volume":"17","author":"Aktas H.","year":"2006","unstructured":"AktasH., Successive sums in smooth groups and smooth cyclic group, Utilitas Math 17 (2006), 23\u201331.","journal-title":"Utilitas Math"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-007-0035-5"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00391-1"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00392-3"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(71)90199-5"},{"issue":"21","key":"e_1_3_1_7_2","first-page":"1005","article-title":"Direct product of fuzzy groups and fuzzy rings","volume":"6","author":"Yetkin E.","year":"2011","unstructured":"YetkinE. and OlgunN., Direct product of fuzzy groups and fuzzy rings, International Mathematical Forum 6(21) (2011), 1005\u20131015.","journal-title":"International Mathematical Forum"},{"key":"e_1_3_1_8_2","first-page":"631","article-title":"Fuzzy group based on fuzzy binary operation","volume":"47","author":"Yuan Xuehai","year":"2004","unstructured":"YuanXuehai and LeeE.S., Fuzzy group based on fuzzy binary operation, An International Journal Computers and Mathematics with Applications 47 (2004), 631\u2013641.","journal-title":"An International Journal Computers and Mathematics with Applications"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151767","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/IFS-151767","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151767","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:10Z","timestamp":1777455550000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/IFS-151767"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,31]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,8,31]]}},"alternative-id":["10.3233\/IFS-151767"],"URL":"https:\/\/doi.org\/10.3233\/ifs-151767","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,8,31]]}}}