The Fuzzy Ideal Under Relation ∈ And Q

In this paper, we investigate the fuzzy set under relation∈and q. In chapter one, we study the (∈,∈∨q)-fuzzy regular,quasi-regular subsemigroups. Based on the idea of quasi-coincident of a fuzzy point with a fuzzy set, we discuss the regular properties and quasi-regular properties of (∈,∈∨q)-fuzzy subsemigroup. In chapter two, we discuss the (∈,∈∨q)-fuzzy k-ideal in semiring.Combining characteristics of different types of (α,β)-fuzzy k-ideals of semirings, we use two methods to obtain the relation between fuzzy k-ideal and (α,β)-fuzzy k-ideals. In chapter three, we discuss the cartesian product of fuzzy left k-ideal. By investigating the fuzzy relations on a semiring and its properties, we discuss the relationship among two fuzzy left k-idealsμ, v andμ×v. We also acquire the properties of the strongest fuzzy relationμv by utilizing these properties.