| Summary: | In this paper, we concentrate on studying the generalization of almost interior Γ-hyperideals in ordered Γ-semihypergroups. The notion of weakly almost interior Γ-hyperideals of ordered Γ-semihypergroups is introduced. This concept generalizes the notion of almost interior Γ-hyperideals in ordered Γ-semihypergroups. Then, the characterization of ordered Γ-semihypergroups having no proper weakly almost interior Γ-hyperideals is provided. Next, we introduce the concept of fuzzy weakly almost interior Γ-hyperideals of ordered Γ-semihypergroups. Also, some properties of fuzzy weakly almost interior Γ-hyperideals are considered. Moreover, the concepts of weakly almost interior Γ-hyperideals and fuzzy weakly almost interior Γ-hyperideals of ordered Γ-semihypergroups are characterized. The connections between strongly prime (resp., prime, semiprime) weakly almost interior Γ-hyperideals and fuzzy strongly prime (resp., prime, semiprime) weakly almost interior Γ-hyperideals in ordered Γ-semihypergroups are presented.
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