In this paper, we introduce the concept of interior Γ-hyperideals of ordered Γ-semihypergroups, which is a generalization of the concept of interior Γ-hyperideals of Γ-semihypergroups to ordered Γ-semihypergroup theory, and investigate its related properties. Furthermore, we define and discuss the fuzzy interior Γ-hyperideals of ordered Γ-semihypergroups. In particular, we give the characterization of fuzzy interior Γ-hyperideal generated by a fuzzy subset in an ordered Γ-semihypergroup. In addition, we consider the concepts of (λ, μ)-fuzzy Γ-hyperideals and (λ, μ)-fuzzy interior Γ-hyperideals in ordered Γ-semihypergroups. Finally, we introduce the notion of (λ, μ)-fuzzy simple ordered Γ-semihypergroups and prove that an ordered Γ-semihypergroup is simple if and only if it is (λ, μ)-fuzzy simple. Especially, characterization of simple ordered Γ-semihypergroups in terms of (λ, μ)-fuzzy interior Γ-hyperideals is given.
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