Several Studies Of The Interval Value Fuzzy Semigroup

Lotfi Zadeh first introduced a very basic concept of a fuzzy set in his com-prehensine papers-《Fuzzy Set》 in1965, and formed a new subject-fuzzy math-ematics on the base of that. Fuzzy set provides a powerful mathematical tools and new methods for modeling situations in which the data are imprecision and uncertainty. Let S be a nonempty subset and [0,1] be a subinterval of real set R. then mapping f:sâ†'[0.1] is called fuzzy subset of S [37]. where (?)x∈S,f(x) is a degree of membership of x. But in reality, sometimes the degrees of membership can’t convey or response completely the essence of the question. Some problems with membership to handle also can produce large deviation. Fortunately, Zadeh also introduced another important conception-interval valued fuzzy set, where using a real interval instead of membership value of object x. in other words, corresponding function values of interval value fuzzy sets are intervals of real numbers instead of the real point, which provided a more adequate description of uncertainty, imprecise and vague than traditional fuzzy set. In this paper, we discuss some fundamental theory and properties of interval value fuzzy set of semigroup algebra. This paper consists of three chapters.In chapter one, we mainly introduce the background knowledge of interval value fuzzy set.In chapter two. we introduce the concepts of interval value fuzzy set and interval value fuzzy left (right, bi) ideal of a semigroup, then definite interval value fuzzy (1,2)-ideal. Some properties of the interval value fuzzy (1,2)-ideals are considered. We prove that an interval value fuzzy set is an interval value fuzzy (1.2)-idcal f if and only if-,f+are also interval value fuzzy (1,2)-ideal of a semigroup. Finally, using a chain of (1,2)-ideal of an interval value fuzzy (1,2)-ideal of a semigroup.In chapter three, we introduce some related concept of interval value fuzzy generalized bi-ideal of a semigroup and definite some operations in them. Finally. some main theorems which characterize the regular semigroups and intra-regular semigroups in terms of interval value fuzzy left (right, bi. generated bi) ideals are given.