Abstract
In this study, we define anti complex fuzzy subgroups and normal anti complex fuzzy subgroups under \(s\)-norms and investigate some of characteristics of them. Later we introduce and study the intersection and composition of them. Next, we define the concept normality between two anti complex fuzzy subgroups by using \(s\)-norms and obtain some properties of them. Finally, we define the image and the inverse image of them under group homomorphisms.
Highlights
Group theory has applications in physics, chemistry, and computer science, and even puzzles like Rubik,s Cube can be represented using group theory
[2–4], especially, some authors considered the fuzzy subgroups with respect to norms [5–7]
We introduce and investigate the normality of μ ∈ ACFS(G) denoted by N ACFS(G)
Summary
Group theory has applications in physics, chemistry, and computer science, and even puzzles like Rubik,s Cube can be represented using group theory. Rosenfeld [2] introduced fuzzy sets in the realm of group theory and formulated the concepts of fuzzy subgroups of a group. Many authors have worked on fuzzy group theory [2–4], especially, some authors considered the fuzzy subgroups with respect to norms [5–7]. Ahmad [8] defined the complex fuzzy subgroup and investigate some of its characteristics. The author by using norms, investigated some properties of fuzzy algebraic structures [9–11]. By using s-norms, we define and investigate some properties of anti complex fuzzy subgroups of group G under s-norm S as ACFS(G). We define the composition and intersection of two μ1, μ2 ∈ ACFS(G) and obtain some of their characteristics. We introduce and investigate the normality of μ ∈ ACFS(G) denoted by N ACFS(G). We show that if μ1, μ2 ∈ ACFS(G) such that μ1 μ2, we show that f (μ1) μ1, μ2 ∈ ACFS(H) such that μ1 μ2, we obtain f −1(μ1) f −1(μ2)
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