Characterizations of Fuzzy Ideals of Semigroups by Soft Sets

Let A be a subsemigroup of a semigroup S and Delta be a nonempty subset of [0, 1]. The aim of this paper is to discuss characterizations of fuzzy subsemigroups, fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy left ideals, fuzzy right ideals and fuzzy ideals of a semigroup S by using soft sets over A x Delta, over A and over Delta. For a nonempty family {f(i) vertical bar i is an element of I} of fuzzy subsets of S, we show equivalent conditions for the fuzzy subset Lambda(i is an element of I) f(i) which is a fuzzy subsemigroup, a fuzzy generalized bi-ideal, a fuzzy bi-ideal, a fuzzy left ideal, a fuzzy right ideal and a fuzzy ideal of S by using soft sets over A x Delta and over Delta. Finally, regular semigroups are characterized by soft sets over S x [0, 1] and over S.