In this paper, we introduce the concepts of (α, β)-fuzzy interior ideals and \((\bar \beta ,\bar \alpha )\)-fuzzy interior ideals of ordered semigroups, where α, β ∈ {egg, qδ, eγ ∨ qδ, eγ ∧ qδ}, and \(\bar \alpha ,\bar \beta \in \{ \overline {\varepsilon _\gamma } ,\overline {q\delta } ,\overline {\varepsilon _\gamma } \vee \overline {q_\delta } ,\overline {\varepsilon _\gamma } \wedge \overline {q_\delta } \} ,\alpha \ne \varepsilon _\gamma \wedge q_\delta \) and \(\bar \beta \ne \overline {\varepsilon _\gamma } \wedge \overline {q_\delta } \), and some related properties are investigated. Special concentration is paid to (eγ, eγ ∨ qδ)-fuzzy interior ideals and (\(\overline {\varepsilon _\gamma } ,\overline {\varepsilon _\gamma } \vee \overline {q_\delta } \))-fuzzy interior ideals.