{"title":"Characterizations of Ordered Semigroups by (\u2208,\u2208 \u2228q)-Fuzzy Ideals","authors":"Jian Tang","volume":68,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":825,"pagesEnd":838,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/13217","abstract":"
Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties. Furthermore, we also define the upper and lower parts of fuzzy subsets of an ordered semigroup S, and investigate the properties of (∈,∈ ∨q)-fuzzy ideals of S. Finally, characterizations of regular ordered semigroups and intra-regular ordered semigroups by means of the lower part of (∈ ,∈ ∨q)-fuzzy left ideals, (∈,∈ ∨q)-fuzzy right ideals and (∈,∈ ∨q)- fuzzy (generalized) bi-ideals are given.<\/p>\r\n","references":"[1] S. K. Bhakat and P. Das, On the definition of a fuzzy subgroup, Fuzzy\r\nSets and Systems, 51(2) (1992), 235-241.\r\n[2] S. K. Bhakat and P. Das, (\u00d4\u00ea\u00ea,\u00d4\u00ea\u00ea \u00d4\u00ea\u00bfq)-fuzzy subgroup, Fuzzy Sets and\r\nSystems, 80(3) (1996), 359-368.\r\n[3] B. 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