Coupled Anti Q-Fuzzy Subgroups using t-Conorms

Abstract

In this paper we study coupled anti Q-fuzzy subgroups of G with respect to t-conorm C. We also discuss the union, normal and direct product of them. Moreover, the homomorphic image and pre-image of them is investigated under group homomorphisms and anti homomorphisms. 1 Some Old and New Notions and Notations Remark 1.1. (a) In this paper we assume G is a group as defined in [1]. (b) We assume the notions of homomorphism and anti-homomorphism as defined in [1]. (c) We assume C : [0, 1]× [0, 1] 7→ [0, 1] is a t-conorm as defined in [1]. (d) By idempotent, we refer to t-conorm C as defined in [1]. Definition 1.2. Let G be an arbitrary group with multiplicative binary operation and identity e. By a fuzzy subset of G×G we mean a function from G×G into [0, 1]. The set of all fuzzy subsets of G×G will be called the [0, 1]-power set of G×G, and will be denoted by [0, 1]G×G. Received: February 1, 2021; Accepted: March 7, 2021 2010 Mathematics Subject Classification: 08A72, 20-XX, 47A30, 20N25, 20K27, 20K30.