$(\lambda,\mu)$-fuzzy interior ideals of ordered $\Gamma$-semigroups

For all $\lambda,\mu\in [0,1]$ such that $\lambda<\mu$, we first introduced the definitions of $(\lambda,\mu)$-fuzzy ideals and $(\lambda,\mu)$-fuzzy interior ideals of an ordered $\Gamma$-semigroup. Then we proved that in regular and in intra-regular ordered semigroups the $(\lambda,\mu)$-fuzzy ideals and the $(\lambda,\mu)$-fuzzy interior ideals coincide. Lastly, we introduced the concept of a $(\lambda,\mu)$-fuzzy simple ordered $\Gamma$-semigroup and characterized the simple ordered $\Gamma$-semigroups in terms of $(\lambda,\mu)$-fuzzy interior ideals.