A novel study on fuzzy ideals and fuzzy filters of ordered *-semigroups

被引：4
作者：
Feng, Xinyang [1 ]
Tang, Jian [2 ]
Davvaz, Bijan [3 ]
Luo, Yanfeng [1 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou, Gansu, Peoples R China
[2] Fuyang Normal Univ, Sch Math & Stat, Fuyang 236037, Anhui, Peoples R China
[3] Yazd Univ, Dept Math, Yazd, Iran
来源：
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS | 2017年 / 33卷 / 01期
关键词：
Ordered *-semigroup; prime fuzzy ideal; weakly prime fuzzy ideal; semiprime fuzzy ideal; fuzzy filter; PRIME; SETS;
D O I：
10.3233/JIFS-161740
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
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.
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页码：423 / 431
页数：9
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