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Discussion on Fuzzy Integral Inequalities via Aumann Integrable Convex Fuzzy-Number Valued Mappings over Fuzzy Inclusion Relation

Author

Listed:
  • Muhammad Bilal Khan

    (Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan)

  • Hakeem A. Othman

    (Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Makkah 24382, Saudi Arabia)

  • Aleksandr Rakhmangulov

    (Department of Logistics and Transportation Systems Management, Nosov Magnitogorsk State Technical University, Magnitogorsk 455000, Russia)

  • Mohamed S. Soliman

    (Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Alia M. Alzubaidi

    (Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Makkah 24382, Saudi Arabia)

Abstract

Convex bodies are naturally symmetrical. There is also a correlation between the two variables of symmetry and convexity. Their use, in either case, has been feasible in recent years because of their interchangeable and similar properties. The proposed analysis provides information on a new class for a convex function which is known as up and down X 1 , X 2 -convex fuzzy-Number valued mappings ( U D - X 1 , X 2 -convex F N V M ). Using this class, we disclosed a number of new versions of integral inequalities. Additionally, we give a number of new related integral inequalities connected to the well-known Hermite-Hadamard-type inequalities. In conclusion, some examples are given to back up and show the value of these new results.

Suggested Citation

  • Muhammad Bilal Khan & Hakeem A. Othman & Aleksandr Rakhmangulov & Mohamed S. Soliman & Alia M. Alzubaidi, 2023. "Discussion on Fuzzy Integral Inequalities via Aumann Integrable Convex Fuzzy-Number Valued Mappings over Fuzzy Inclusion Relation," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1356-:d:1093832
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    References listed on IDEAS

    as
    1. Fuzhang Wang & Muhammad Nawaz Khan & Imtiaz Ahmad & Hijaz Ahmad & Hanaa Abu-Zinadah & Yu-Ming Chu, 2022. "Numerical Solution Of Traveling Waves In Chemical Kinetics: Time-Fractional Fishers Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(02), pages 1-11, March.
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    7. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann Integrals," Mathematics, MDPI, vol. 10(18), pages 1-18, September.
    8. İmdat İşcan, 2014. "Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions," Journal of Mathematics, Hindawi, vol. 2014, pages 1-10, June.
    9. Muhammad Bilal Khan & Hakeem A. Othman & Michael Gr. Voskoglou & Lazim Abdullah & Alia M. Alzubaidi, 2023. "Some Certain Fuzzy Aumann Integral Inequalities for Generalized Convexity via Fuzzy Number Valued Mappings," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    10. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Class of Preinvex Fuzzy Mappings and Related Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-20, October.
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