Document Type: Research Paper
Department of Mathematics and Physics, Wuyi University , Jiangmen, Guangdong, 529020, P.R.China
Jian Tang\ School of Mathematics and Computational Science, Fuyang Normal College, Fuyang, Anhui, 236041, P.R.China
Let $S$ be an ordered semigroup. A fuzzy subset of $S$ is an
arbitrary mapping from $S$ into $[0,1]$, where $[0,1]$ is the
usual interval of real numbers. In this paper, the concept of fuzzy
generalized bi-ideals of an ordered semigroup $S$ is introduced.
Regular ordered semigroups are characterized by means of fuzzy left
ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.
Finally, two main theorems which characterize regular ordered
semigroups and intra-regular ordered semigroups in terms of fuzzy
left ideals, fuzzy right ideals, fuzzy bi-ideals or fuzzy
quasi-ideals are given. The paper shows that one can pass from
results in terms of fuzzy subsets in semigroups to ordered
semigroups. The corresponding results of unordered semigroups are