Several Studies Of The Generalized Fuzzy Super Ring

The theory of algebraic hyperstructure enriches the theory of the classical algebraic theory, provides many new methods and supports further development of theory of algebra.Combination of theory of fuzzy set and theory of algebraic hyperstructure gives new ideas and methods to the research on algebraic hyperstructure theory. This generates a new way to study algebraic theory.This paper according to the research of the predecessor basis. firstly we define the notion of (m,n) hyperrings that is a generalization of the notion of hyperrings and is different from Krasner(m,n) hyperrings. Then we introduce the notion of Krasner(m,n) fuzzy hyperrings. By use of lever cutest we studied the (m,n) hyperrings and Krasner(m,n) fuzzy hyperrings are steady under homomorphisms, and research the connections among regular relation, strong regular relation and (m,n) hyperideals. So we can get the (m,n) hyperideals by strong regular relation. Then we search the quotient structure of (m,n) hyperrings by use of regular relation and strong regular relation. And get the sufficient and necessary condition of the quotient structure of (m,n) hyperrings and the quotient of (m,n) hyperrings. Secondly, we discuss some properties about Γ-Hv-rings which are the most generalization of the notion of hyperrings. We introduce the notion of (λ,μ)-Γ-Hv-fuzzy ideals by using of generalization of Γ-Hv-fuzzy ideals. We study the relation of fuzzy congruences and strong fuzzy congruences,and the relation of regular relation and strong regular relation.Then we give the sufficient and necessary condition of conversion between them. And we research the relationship among (λ,μ)-Γ-Hv-fuzzy ideals, fuzzy congruences and strong fuzzy congruences over ΓHv-rings. We can get fuzzy ideals by use of strong fuzzy congruences over Γ-Hv-rings.