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regular ordered semigroups and intra-regular ordered semigroups in terms of fuzzy subsets

xiang-yun xie, jian tang

Abstract

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper, the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two main theorems which characterize regular orderedsemigroups and intra-regular ordered semigroups in terms of fuzzyleft ideals, fuzzy right ideals, fuzzy bi-ideals or fuzzyquasi-ideals are given. the paper shows that one can pass fromresults in terms of fuzzy subsets in semigroups to orderedsemigroups. the corresponding results of unordered semigroups arealso obtained.

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