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2013•Journal of Liaocheng UniversityRequires access

(λ,μ)-Fuzzy Homomorphism of Group

Hao Cui-xi

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Abstract

Fuzzy homomorphism is a spread of the corresponding classical concept as an important concept of fuzzy algebra,and it can be produced by different fuzzy mappings.This paper presents a concept of(λ,μ)-fuzzy mapping and gives the definition of(λ,μ)-fuzzy homomorphism of groups.What's more,it studies the relationships between the(λ,μ)-fuzzy subgroups and some properties under the(λ, μ)-fuzzy homomorphism.Finally,this paper establishes the fundamental theorem of(λ,μ)-fuzzy homomorphism.

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What this paper is about

Fuzzy homomorphism is a spread of the corresponding classical concept as an important concept of fuzzy algebra,and it can be produced by different fuzzy mappings.This paper presents a concept of(λ,μ)-fuzzy mapping and gives the definition of(λ,μ)-fuzzy homomorphism of groups.What's more,it studies the relationships between the(λ,μ)-fuzzy subgroups and some properties under the(λ, μ)-fuzzy homomorphism.Finally,this paper establishes the fundamental theorem of(λ,μ)-fuzzy homomorphism.

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Available abstract

Fuzzy homomorphism is a spread of the corresponding classical concept as an important concept of fuzzy algebra,and it can be produced by different fuzzy mappings.This paper presents a concept of(λ,μ)-fuzzy mapping and gives the definition of(λ,μ)-fuzzy homomorphism of groups.What's more,it studies the relationships between the(λ,μ)-fuzzy subgroups and some properties under the(λ, μ)-fuzzy homomorphism.Finally,this paper establishes the fundamental theorem of(λ,μ)-fuzzy homomorphism.

Key concepts: Homomorphism, Mathematics, Fuzzy logic, Algebra homomorphism, Fuzzy subalgebra, Algebra over a field, Group (periodic table), Fuzzy set

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