Some Certain Fuzzy Aumann Integral Inequalities for Generalized Convexity via Fuzzy Number Valued Mappings

Muhammad Bilal Khan, Hakeem A. Othman, Michael Gr. Voskoglou (), Lazim Abdullah () and Alia M. Alzubaidi
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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
Michael Gr. Voskoglou: Mathematical Sciences, Graduate TEI of Western Greece, 26334 Patras, Greece
Lazim Abdullah: Management Science Research Group, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia
Alia M. Alzubaidi: Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Makkah 24382, Saudi Arabia

Mathematics, 2023, vol. 11, issue 3, 1-23

Abstract: The topic of convex and nonconvex mapping has many applications in engineering and applied mathematics. The Aumann and fuzzy Aumann integrals are the most significant interval and fuzzy operators that allow the classical theory of integrals to be generalized. This paper considers the well-known fuzzy Hermite–Hadamard (HH) type and associated inequalities. With the help of fuzzy Aumann integrals and the newly introduced fuzzy number valued up and down convexity ( U D -convexity), we increase this mileage even further. Additionally, with the help of definitions of lower U D -concave (lower U D -concave) and upper U D -convex (concave) fuzzy number valued mappings ( F N V M s), we have gathered a sizable collection of both well-known and new extraordinary cases that act as applications of the main conclusions. We also offer a few examples of fuzzy number valued U D -convexity to further demonstrate the validity of the fuzzy inclusion relations presented in this study.

Keywords: fuzzy number valued mapping; fuzzy Aumann integral; up and down convex fuzzy number valued mapping; Hermite–Hadamard inequality; Hermite–Hadamard–Fejér inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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