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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