Affiliations: [a] School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, P.R. China | [b] School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui, P.R. China | [c] Department of Mathematics, Yazd University, Yazd, Iran
Correspondence:
[*]
Corresponding author. Jian Tang, School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui 236037, P.R. China. Tel./Fax: +86 0558 2591133; E-mail: tangjian0901@126.com.
Abstract: In this paper, we study the ordered *-semigroups in terms of fuzzy subsets in detail and define a unary operation * on the set of all the fuzzy subsets of an ordered *-semigroup S, which is a key notion to introduce the concepts of prime, weakly prime and semiprime fuzzy ideals of S. Furthermore, we establish the relationships among these three types of fuzzy ideals and give some characterizations of intra-regular ordered *-semigroups in terms of fuzzy ideals. Finally, we define and study the fuzzy filters of an ordered *-semigroup. In particular, we discuss the relationships between the filters and the fuzzy filters in ordered *-semigroups.
Keywords: Ordered *-semigroup, prime fuzzy ideal, weakly prime fuzzy ideal, semiprime fuzzy ideal, fuzzy filter
