The Connections of Strongest Fuzzy Γ-ideals on Ternary Γ-semigroups (European Journal of Pure and Applied Mathematics, 2024)
The fuzzy relation $R_μ$ on $μ$, where $μ$ is a fuzzy set of a set $X$, is called a strongest fuzzy relation on $X$ if $R_μ(x,y)=\min\{μ(x),μ(y)\}$, for all $x,y\in X$. The notion of strongest fuzzy relations will be applied in our investigation of ternary $Γ$-semigroups. In order to achieve this, we will define the concepts of strongest fuzzy ternary $Γ$-subsemigroups, strongest fuzzy $Γ$-ideals (resp. left, right, and lateral), and strongest fuzzy bi-$Γ$-ideals on ternary $Γ$-semigroups. Then, we study the connections and characterizations of these concepts in ternary $Γ$-semigroups.
Keywords: Strongest fuzzy relation; Strongest fuzzy Γ-ideal; Γ-Ideal; Ternary Γ-semigroup