On A New Notion of Anti-Fuzzy Normal Subgroup

Abstract

Zadeh defined a fuzzy set mathematically by assigning to each individual in the universe of discourse a value representing its grade of membership in the fuzzy set. This grade corresponds to the degree to which that individual is “similar” or “compatible” with the concept represented by a fuzzy set. Rosenfeld was the first researcher who applied this concept in the realm of group theory and formulated the notion of fuzzy subgroups [5]. Mukherjee and Bhattacharya studied fuzzy normal subgroups [3]. Later on, in [1], R. Biswas enunciated the concept of the anti-fuzzy subgroup. Anti-fuzzy subgroups were also studied by Gayen, Jha, Singh, and Prasad [2].

Our endeavor in this paper revolves around the work proposed by R. Biswas and Gayen, Jha, Singh, Prasad and Mukherjee, and Bhattacharya. Here, we have presented the redefined version of anti-fuzzy normal subgroups and have derived some interesting results based on our proposed notion of anti-fuzzy normal subgroups, along with some exciting examples.