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.
Highlights
(b) We assume the notions of homomorphism and anti-homomorphism as defined in [1]
The set of all anti Q-fuzzy subgroups of G × G with respect to t-conorm C will be denoted by AQF SC(G × G)
(b) If β(x, m, q) ≥ μ(eG, eG, q), β ∈ AQF SC(H × H) for all (x, m) ∈ H and q ∈ Q
Summary
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]. Μ ∈ [0, 1](G×G)×Q will be called an anti Q-fuzzy subgroup of G × G with respect to t-conorm C if the following conditions are satisfied (a) μ(xy, mv, q) ≤ C[μ(x, m, q), μ(y, v, q)] (b) μ(x−1, m−1, q) ≤ μ(x, m, q) for all (x, m), (y, v) ∈ G × G, and q ∈ Q. The set of all anti Q-fuzzy subgroups of G × G with respect to t-conorm C will be denoted by AQF SC(G × G). (Compare with Proposition 2.3[1]) Let G be a group, and H be a nonempty subset of G × G. N AQF SC(G × G) will denote the set of all normal anti Q-fuzzy subgroups of G × G with respect to t-conorm C
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