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Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals

Author

Listed:
  • Mesfer H. Alqahtani

    (Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk 48322, Saudi Arabia)

  • Der-Chyuan Lou

    (Department of Computer Science and Information Engineering, Chang Gung University, Taoyuan 33302, Taiwan
    Stroke Center and Department of Neurology, Chang Gung Memorial Hospital, Linkou, Taoyuan 33302, Taiwan)

  • Fahad Sikander

    (Department of Basics Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Jeddah 23442, Saudi Arabia)

  • Yaser Saber

    (Department of Mathematics, College of Science Al-Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah 11952, Saudi Arabia)

  • Cheng-Chi Lee

    (Department of Library and Information Science, Fu Jen Catholic University, New Taipei City 24205, Taiwan
    Department of Computer Science and Information Engineering, Fintech and Blockchain Research Center, Asia University, Taichung 41354, Taiwan)

Abstract

This study presents new fuzzy adaptations of Ostrowski’s integral inequalities through a novel class of convex fuzzy-valued mappings defined over a harmonic convex set, avoiding the use of the Sugeno integral. These innovative inequalities generalize the recently developed interval forms of real-valued Ostrowski inequalities. Their formulations incorporate integrability concepts for fuzzy-valued mappings (FVMs), applying the Kaleva integral and a Kulisch–Miranker fuzzy order relation. The fuzzy order relation is constructed via a level-wise approach based on the Kulisch–Miranker order within the fuzzy number space. Additionally, numerical examples illustrate the effectiveness and significance of the proposed theoretical model. Various applications are explored using different means, and some complex cases are derived.

Suggested Citation

  • Mesfer H. Alqahtani & Der-Chyuan Lou & Fahad Sikander & Yaser Saber & Cheng-Chi Lee, 2024. "Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals," Mathematics, MDPI, vol. 12(22), pages 1-29, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3495-:d:1517072
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    References listed on IDEAS

    as
    1. Khan, Muhammad Bilal & Othman, Hakeem A. & Santos-García, Gustavo & Saeed, Tareq & Soliman, Mohamed S., 2023. "On fuzzy fractional integral operators having exponential kernels and related certain inequalities for exponential trigonometric convex fuzzy-number valued mappings," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
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