IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i6p1356-d1093832.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/6/1356/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/6/1356/
    Download Restriction: no
    ---><---

    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.
    2. Mihai, Marcela V. & Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some integral inequalities for harmonic h-convex functions involving hypergeometric functions," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 257-262.
    3. Yanrong An & Guoju Ye & Dafang Zhao & Wei Liu, 2019. "Hermite-Hadamard Type Inequalities for Interval ( h 1 , h 2 )-Convex Functions," Mathematics, MDPI, vol. 7(5), pages 1-9, May.
    4. 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).
    5. 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.
    6. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Muhammad Bilal Khan & Aleksandr Rakhmangulov & Najla Aloraini & Muhammad Aslam Noor & Mohamed S. Soliman, 2023. "Generalized Harmonically Convex Fuzzy-Number-Valued Mappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    2. 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.
    3. 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.
    4. 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.
    5. Waqar Afzal & Alina Alb Lupaş & Khurram Shabbir, 2022. "Hermite–Hadamard and Jensen-Type Inequalities for Harmonical ( h 1 , h 2 )-Godunova–Levin Interval-Valued Functions," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    6. Yahya Almalki & Waqar Afzal, 2023. "Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr - h -Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    7. 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).
    8. Muhammad Tariq & Soubhagya Kumar Sahoo & Sotiris K. Ntouyas & Omar Mutab Alsalami & Asif Ali Shaikh & Kamsing Nonlaopon, 2022. "Some New Mathematical Integral Inequalities Pertaining to Generalized Harmonic Convexity with Applications," Mathematics, MDPI, vol. 10(18), pages 1-21, September.
    9. 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.
    10. Muhammad Bilal Khan & Jorge E. Macías-Díaz & Savin Treanțǎ & Mohamed S. Soliman, 2022. "Some Fejér-Type Inequalities for Generalized Interval-Valued Convex Functions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    11. Tareq Saeed & Muhammad Bilal Khan & Savin Treanță & Hamed H. Alsulami & Mohammed Sh. Alhodaly, 2023. "Study of Log Convex Mappings in Fuzzy Aunnam Calculus via Fuzzy Inclusion Relation over Fuzzy-Number Space," Mathematics, MDPI, vol. 11(9), pages 1-16, April.
    12. Gustavo Santos-García & Muhammad Bilal Khan & Hleil Alrweili & Ahmad Aziz Alahmadi & Sherif S. M. Ghoneim, 2022. "Hermite–Hadamard and Pachpatte Type Inequalities for Coordinated Preinvex Fuzzy-Interval-Valued Functions Pertaining to a Fuzzy-Interval Double Integral Operator," Mathematics, MDPI, vol. 10(15), pages 1-25, August.
    13. Fu, Xinjie & Wang, JinRong, 2022. "Dynamic stability and optimal control of SISqIqRS epidemic network," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    14. 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.
    15. Peide Liu & Xinli You, 2018. "Some linguistic neutrosophic Hamy mean operators and their application to multi-attribute group decision making," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-26, March.
    16. Eghlimi, Hadi & Asgari, Mohammad Sadegh, 2023. "A study of the time-fractional heat equation under the generalized Hukuhara conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    17. Muhammad Aamir Ali & Fongchan Wannalookkhee & Hüseyin Budak & Sina Etemad & Shahram Rezapour, 2022. "New Hermite–Hadamard and Ostrowski-Type Inequalities for Newly Introduced Co-Ordinated Convexity with Respect to a Pair of Functions," Mathematics, MDPI, vol. 10(19), pages 1-24, September.
    18. Imran Abbas Baloch & İmdat İşcan, 2015. "Some Ostrowski Type Inequalities for Harmonically -Convex Functions in Second Sense," International Journal of Analysis, Hindawi, vol. 2015, pages 1-9, October.
    19. Xu, Hang, 2023. "A generalized analytical approach for highly accurate solutions of fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    20. Kang, Daekook & Devi, S. Aicevarya & Felix, Augustin & Narayanamoorthy, Samayan & Kalaiselvan, Samayan & Balaenu, Dumitru & Ahmadian, Ali, 2022. "Intuitionistic fuzzy MAUT-BW Delphi method for medication service robot selection during COVID-19," Operations Research Perspectives, Elsevier, vol. 9(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1356-:d:1093832. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.