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The fuzzy relation R_ on, where is a fuzzy set of a set X, is called a strongest fuzzy relation on X if R_ (x, y) =\ (x), (y) \, for all x, y X. The notion of strongest fuzzy relations will be applied in our investigation of ternary -semigroups. In order to achieve this, we will define the concepts of strongest fuzzy ternary -subsemigroups, strongest fuzzy -ideals (resp. left, right, and lateral), and strongest fuzzy bi--ideals on ternary -semigroups. Then, we study the connections and characterizations of these concepts in ternary -semigroups.
Nakkhasen et al. (2024) studied this question.