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Characterizations of ordered semigroups by (ε γ , ε γ q δ)-fuzzy interior ideals

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Abstract

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 ∈ {ε gg , , ε γ , ε γ }, 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 (ε γ , ε γ )-fuzzy interior ideals and (\(\overline {\varepsilon _\gamma } ,\overline {\varepsilon _\gamma } \vee \overline {q_\delta } \))-fuzzy interior ideals.

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Correspondence to Faiz Muhammad Khan.

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Submitted by P.N. Ivanshin

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Khan, F.M., Khan, A. & Sarmin, N.H. Characterizations of ordered semigroups by (ε γ , ε γ q δ)-fuzzy interior ideals. Lobachevskii J Math 32, 278–288 (2011). https://doi.org/10.1134/S1995080211040123

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  • DOI: https://doi.org/10.1134/S1995080211040123

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