Rough semigroups and rough fuzzy semigroups based on fuzzy ideals

Open Mathematics

Zhan Jianming¹  Wang Qiumei¹ 

[1] Department of Mathematics, Hubei University for Nationalities, Enshi, 445000, China;

关键词: fuzzy ideal;    t-level set;    rough semigroup;    rough fuzzy semigroup;    rough (prime) ideal;    rough fuzzy (prime) ideal;    20n20;    16y99;   

DOI  :  10.1515/math-2016-0102

来源: DOAJ

【 摘 要 】

In this paper, we firstly introduce a special congruence relation U(μ, t) induced by a fuzzy ideal μ in a semigroup S. Then we define the lower and upper approximations based on a fuzzy ideal in semigroups. We can establish rough semigroups, rough ideals, rough prime ideals, rough fuzzy semigroups, rough fuzzy ideals and rough fuzzy prime ideals according to the definitions of rough sets and rough fuzzy sets. Furthermore, we shall consider the relationships among semigroups and rough semigroups, fuzzy semigroups and rough fuzzy semigroups, and some relative properties are also discussed.

【 授权许可】

Unknown