A Study Of (λ,μ)-Anti-Fuzzy Subgroup

Based on the basic conclusions of(λ,μ)-fuzzy subgroup and anti-fuzzy subgroup,we fur-ther investigate(λ,μ)-anti-fuzzy subgroup,(λ,μ)-anti-fuzzy normal subgroup and(λ,μ)-anti-fuzzy homomorphism,finally we get a series of significant results.The paper mainly contains the following three parts:In the first part,we study the structure of(λ,μ)-anti-fuzzy subgroup and(λ,μ)-anti-fuzzy normal subgroup.Firstly,we discuss(λ,μ)-anti-fuzzy subgroup of G distribution of membership degree of the different elements of G.Secondly,we study the(λ,μ)-anti-fuzzy normal subgroup of G the distribution of membership degree on the different elements of G.The main results contain the following three parts:1.Let A be a(λ,μ)-anti-fuzzy subgroup of G and λ<A(e)<μ,then A(e)≤<A(x)holds for all x ∈G and A(x)= A(e)holds for all x∈AA(e).2.Let A be a fuzzy set of G,then A is a(λ,μ)-anti-fuzzy subgroup of G if and only if Aα≠(?)is a subgroup of G for all α∈[λ,μ).3.Let A be a(λ,μ)-anti-fuzzy subgroup of G,then A is a(λ,μ)-anti-fuzzy normal subgroup of G if and only if A([x,y])Λμ≤A(x)(?)λ for all x,y∈G.In this two parts,(λ,μ)-anti-fuzzy subgroup and normal subgroup structure of cyclic group and Abelian group are discussed in detail and gives the corresponding results:Let G =...