Abstract
Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory. The concept of 'intuitionistic fuzzy set' (IFS) was introduced by Atanassov as a generalization of the concept fuzzy set by gives both a degree of membership and the degree of non-membership. As for fuzzy sets, the degree of membership is a real number between 0 and 1. This is also the case for the degree of non-membership, and further the sum of these two degrees is not greater than 1. Since fuzzy bi-ideal play an important role in the study of smigroup structures. The purpose of this paper is to initiate and study the intuitionistic fuzzification on the concept of several ideals in a semigroups S and investigate the basic theorem of intuitionistic fuzzy bi-ideals and discuss the relationships of left( resp. right and completely regular) semigroups in terms of intuitionistic fuzzy bi-ideals. For any homomorphisim f from a semigroup S to semigroup T if B=(μ_(B ),γ_B) is an intuitionistic fuzzy bi-ideal of T, then the preimage f^(-1) (B)=(f^(-1) (μ_(B ) ),f^(-1) (γ_B )) of B under f is an intuitionistic fuzzy bi-ideal of semigroup S.