Product of (𝜆, 𝜇)-Multifuzzy Subgroups of A Group

Abstract

“In 1965, L.A. Zadeh[20] introduced the notion of fuzzy set of any non empty set. In 1996, Bhakat [5] and Das[7] proposed the concept of an (∈, ∈ ∨𝑞)-fuzzy subgroup. In 2003, Yuan et al. and Yuying Li ed al. [18,19] defined the notion of (𝜆, 𝜇)-fuzzy subgroups, which is an extension of (∈, ∈ ∨𝑞)-fuzzy subgroup. As in the case of fuzzy group, some counterparts of classic concepts can be found for (𝜆, 𝜇)-fuzzy subgroups. For instance, (𝜆, 𝜇)- fuzzy normal subgroups and (𝜆, 𝜇)-fuzzy quotient groups are defined and their elementary properties are investigated, and an equivalent characterization of (𝜆, 𝜇)-fuzzy normal subgroups was presented in [18,19]. However, there is much more research on (𝜆, 𝜇)-fuzzy subgroups if we consider rich results both in the classic group theory and the fuzzy group theory in the sense of Rosenfeld[11]. After several years, S.Sabu and T.V.Ramakrishnan[12,13] proposed the theory of multi fuzzy sets in terms of multi dimensional membership functions. Aktas. H and Cagman. N[1] proposed the product of fuzzy subgroups of a group[2]. The notion of (𝜆, 𝜇)-multi fuzzy subgroup was introduced by the author[4]. R.Muthuraj ed al.[9] Proposed anti product of multi fuzzy subgroups of a group. In this paper we define product of (𝜆, 𝜇)-multi fuzzy subgroups of a group and study some of their related properties.”