Generalized fuzzy n-ary subpolygroups endowed with interval valued membership functions

Abstract

Recently, fuzzy n-ary polygroups were introduced and analyzed by Davvaz, Corsini and Leoreanu-Fotea. Fuzzy n-ary polygroups are suitable generalizations of n-ary polygroups and a special case of fuzzy n-ary hypergroups. The aim of this paper is to introduce the notion of an interval-valued fuzzy n-ary subpolygroup of an n-ary subpolygroup and to extend the fuzzy n-ary subpolygroup to interval-valued (∈, ∈, ∨q)-fuzzy n-ary subpolygroup. We also consider the concept of implication-based interval-valued fuzzy n-ary sub-polygroup in an n-ary polygroup, in particular, the implication operators in £ukasiewicz system of continuous-valued logic are discussed.