On Fuzzy Generalizations Of Some Results In Finite

Abstract

In this thesis, we have investigated some basic results of fuzzy group theory by constructing various examples. In particular, we have studied the notions of fuzzy subgroup, normal fuzzy subgroup, fuzzy coset and fuzzy quotient group and have elaborated these concepts through examples. We have proved that if ξ1 and ξ2 are fuzzy subgroups of a group G, then intersection of ξ1 and ξ2 is again a fuzzy subgroup of G. Also, we have shown that for two fuzzy subgroups ξ1 and ξ2 of a group G, if ξ1 is a normal fuzzy subgroup of ξ1, then ξ1 ∩ ξ2 is a normal fuzzy subgroup of ξ1 ∩ ν. Furthermore, we have defined the concept of a fuzzy subgroup of a fuzzy group. We have formulated the notion of an m-polar fuzzy group as a generalization of a fuzzy group. Moreover, we have introduced m-polar fuzzy analogs of some results in fuzzy group theory