Certain Results on m-polar Fuzzy Groups

Abstract

In this thesis we have developed some fundamental results from group theory to fuzzy and m-polar fuzzy groups. We have defined some basic characteristics of fuzzy groups and have provided the m-polar fuzzy analogues of fuzzy subsets, groups, level sets, and cosets. We have investigated an equivalence relation to distinguish whether a m-polar fuzzy subgroup of a group G is equivalent to any other m-polar fuzzy subgroup of that same group G, or not. We determined the maximal chains and a general formula for quaternion and dihedral groups to give the cardinality of their fuzzy and m-polar fuzzy subgroups. We intro duced aninequality which gives quantitative relationship between maximal chains, level subgroups and fuzzy subgroups. Moreover, we mainly constructed the m-polar fuzzy analogues of isomorphism theorems and butterfly lemma.