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