The Measures Of Fuzzy Subgroup And Fuzzy Normal Subgroup Based On T-Norms

In this paper, we investigate properties of the measure of a fuzzy subgroup based on a general t-norm*. The involved work is with the*-fuzzy subgroup degree and*-normal fuzzy subgroup degree.In the study of the*-fuzzy subgroup degree, we firstly present some basic properties including mainly the*-fuzzy subgroup degree of the intersection of an arbitrary family of fuzzy subsets, the*-fuzzy subgroup degree of the*’-intersection of two fuzzy subsets if*’dominates*and the*-fuzzy subgroup degrees of the image and preimage of a fuzzy subset under a homomorphism.Then we discuss the*-fuzzy subgroup degrees of two types of products (*-product and*-direct product). Under the condition that*’dominates*, we investigate the relationship between the*-fuzzy subgroup degrees of two fuzzy subsets of a commutative group and that of their*’-product, and the*-fuzzy subgroup degree of the*-product of two fuzzy subsets of a general group. Meanwhile, we study the relationship between the*-fuzzy subgroup degrees of two fuzzy subsets and that of their*’-direct product with the same domination condition.In addition to the investigation of the*-fuzzy subgroup degree, we also give the definition of an*-fuzzy normal subgroup and present an indicator to measure the degree to which a fuzzy subset is an*-fuzzy normal subgroup. The similar research to the*-fuzzy subgroup degree is carried out for the*-fuzzy normal subgroup degree.