(untitled) (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)={μ(x),μ(y)}, for all x,yX. 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.