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

Document Type: Research Paper

Authors

1 Department of Mathematics and Physics, Wuyi University , Jiangmen, Guangdong, 529020, P.R.China

2 Jian Tang\ School of Mathematics and Computational Science, Fuyang Normal College, Fuyang, Anhui, 236041, P.R.China

Abstract

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
also obtained.

Keywords