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Some New Properties of Convex Fuzzy-Number-Valued Mappings on Coordinates Using Up and Down Fuzzy Relations and Related Inequalities

Author

Listed:
  • Muhammad Bilal Khan

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

  • Ali Althobaiti

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

  • Cheng-Chi Lee

    (Research and Development Center for Physical Education, Health, and Information Technology, Department of Library and Information Science, Fu Jen Catholic University, New Taipei City 24205, Taiwan
    Department of Computer Science and Information Engineering, Asia University, Taichung 41354, Taiwan)

  • Mohamed S. Soliman

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

  • Chun-Ta Li

    (Bachelor’s Program of Artificial Intelligence and Information Security, Graduate Institute of Applied Science and Engineering, Fu Jen Catholic University, New Taipei City 24206, Taiwan)

Abstract

The symmetric function class interacts heavily with other types of functions. One of these is the convex function class, which is strongly related to symmetry theory. In this study, we define a novel class of convex mappings on planes using a fuzzy inclusion relation, known as coordinated up and down convex fuzzy-number-valued mapping. Several new definitions are introduced by placing some moderate restrictions on the notion of coordinated up and down convex fuzzy-number-valued mapping. Other uncommon examples are also described using these definitions, which can be viewed as applications of the new outcomes. Moreover, Hermite–Hadamard–Fejér inequalities are acquired via fuzzy double Aumann integrals, and the validation of these outcomes is discussed with the help of nontrivial examples and suitable choices of coordinated up and down convex fuzzy-number-valued mappings.

Suggested Citation

  • Muhammad Bilal Khan & Ali Althobaiti & Cheng-Chi Lee & Mohamed S. Soliman & Chun-Ta Li, 2023. "Some New Properties of Convex Fuzzy-Number-Valued Mappings on Coordinates Using Up and Down Fuzzy Relations and Related Inequalities," Mathematics, MDPI, vol. 11(13), pages 1-23, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2851-:d:1179133
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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).
    2. 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.
    3. Khan, Muhammad Bilal & Santos-García, Gustavo & Noor, Muhammad Aslam & Soliman, Mohamed S., 2022. "Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Hongxin Bai & Muhammad Shoaib Saleem & Waqas Nazeer & Muhammad Sajid Zahoor & Taiyin Zhao & Viliam Makis, 2020. "Hermite-Hadamard- and Jensen-Type Inequalities for Interval h1,h2 Nonconvex Function," Journal of Mathematics, Hindawi, vol. 2020, pages 1-6, April.
    5. Fangfang Shi & Guoju Ye & Dafang Zhao & Wei Liu, 2020. "Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    6. Muhammad Bilal Khan & Savin Treanțǎ & Mohamed S. Soliman & Kamsing Nonlaopon & Hatim Ghazi Zaini, 2022. "Some New Versions of Integral Inequalities for Left and Right Preinvex Functions in the Interval-Valued Settings," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    7. Chu, Yu-Ming & Xia, Wei-Feng & Zhang, Xiao-Hui, 2012. "The Schur concavity, Schur multiplicative and harmonic convexities of the second dual form of the Hamy symmetric function with applications," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 412-421.
    8. İmdat İşcan & Mehmet Kunt, 2016. "Hermite-Hadamard-Fejér Type Inequalities for Quasi-Geometrically Convex Functions via Fractional Integrals," Journal of Mathematics, Hindawi, vol. 2016, pages 1-7, February.
    9. Kin Keung Lai & Jaya Bisht & Nidhi Sharma & Shashi Kant Mishra, 2022. "Hermite-Hadamard-Type Fractional Inclusions for Interval-Valued Preinvex Functions," Mathematics, MDPI, vol. 10(2), pages 1-16, January.
    10. Du, Tingsong & Zhou, Taichun, 2022. "On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    11. Muhammad Bilal Khan & Gustavo Santos-García & Hatim Ghazi Zaini & Savin Treanță & Mohamed S. Soliman, 2022. "Some New Concepts Related to Integral Operators and Inequalities on Coordinates in Fuzzy Fractional Calculus," Mathematics, MDPI, vol. 10(4), pages 1-26, February.
    12. Dafang Zhao & Guohui Zhao & Guoju Ye & Wei Liu & Silvestru Sever Dragomir, 2021. "On Hermite–Hadamard-Type Inequalities for Coordinated h -Convex Interval-Valued Functions," Mathematics, MDPI, vol. 9(19), pages 1-14, September.
    13. 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.
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