Intuitionistic fuzzy sets in gamma-semigroups

Abstract

The notion of a fuzzy set in a set was introduced by L. A. Zadeh [10], and since then this concept has been applied to various algebraic structures. K. T. Atanassov [1] defined the notion of an intuitionistic fuzzy set, as a concept more general than a fuzzy set (see also [2]). Using fuzzy ideals, N. Kuroki [5] discussed characterizations of semigroups (see also [6]). K. H. Kim and Y. B. Jun [3] considered the intuitionistic fuzzification of the notion of several ideals in a semigroup, and investigated some properties of such ideals (see also [4]). M. K. Sen and N. K. Saha [9] defined the concept of a Gamma-semigroup, and established a relation between regular Gamma-semigroup and Gamma-group (see also [7], (8]). In this paper, we introduce the notion of an intuitionistic fuzzy Gamma-ideal of a Gamma-semigroup, and we investigate some properties connected with intuitionistic fuzzy Gamma-ideals in a Gamma-semigroup.