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

Muhammad Bilal Khan (), Hakeem A. Othman, Aleksandr Rakhmangulov (), Mohamed S. Soliman 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
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

Mathematics, 2023, vol. 11, issue 6, 1-20

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.

Keywords: fuzzy aumann integral; up and down (? 1 , ? 2 )-convex fuzzy-number valued mappings; Hermite-Hadamard type inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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