Anti Homomorphism in Fuzzy Subgroups

Abstract

On the basis of fuzzy sets introduced by L.A. Zadeh, we first gave the definition of fuzzy subgroups and fuzzy normal subgroups. This paper proves a necessary and sufficient condition of fuzzy subgroup (normal subgroup) to be fuzzy subgroup (normal subgroup). We introduced the notion of anti fuzzy subgroups and their related properties. Finally, behaviour of these anti fuzzy subgroups (normal subgroups) under group homomorphism have been discussed. We define a notion of homomorphism and anti homomorphism of multi L-fuzzy subgroup and investigate some of its properties. This paper contains the definition and result of anti L-fuzzy normal subgroup is being given using homomorphism and anti homomorphism.