Fuzzy homomorphism theorems on groups
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In this paper we introduce the notion of a fuzzy kernel of a fuzzy homomorphism on groups and we show that it is a fuzzy normal subgroup of the domain group. Conversely, we also prove that any fuzzy normal subgroup is a fuzzy kernel of some fuzzy epimorphism, namely the canonical fuzzy epimorphism. Finally, we formulate and prove the fuzzy version of the fundamental theorem of homomorphism and those isomorphism theorems.
Abstract
In this paper we introduce the notion of a fuzzy kernel of a fuzzy homomorphism on groups and we show that it is a fuzzy normal subgroup of the domain group. Conversely, we also prove that any fuzzy normal subgroup is a fuzzy kernel of some fuzzy epimorphism, namely the canonical fuzzy epimorphism. Finally, we formulate and prove the fuzzy version of the fundamental theorem of homomorphism and those isomorphism theorems.
참고문헌 (15)
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