Discussion on Fuzzy Integral Inequalities via Aumann Integrable Convex Fuzzy-Number Valued Mappings over Fuzzy Inclusion Relation-Reference-Cited by-同舟云学术

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

Published:2023-03-10 Issue:6 Volume:11 Page:1356
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Khan Muhammad¹^ORCID,Othman Hakeem²^ORCID,Rakhmangulov Aleksandr³^ORCID,Soliman Mohamed⁴^ORCID,Alzubaidi Alia²

Affiliation:

1. Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan

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

3. Department of Logistics and Transportation Systems Management, Nosov Magnitogorsk State Technical University, Magnitogorsk 455000, Russia

4. Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, 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 X1,X2-convex fuzzy-Number valued mappings (UD-X1,X2-convex FNVM). 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.

Funder

Scientific Research at Umm Al-Qura University

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/6/1356/pdf

Reference104 articles.

1. Niculescu, C.P., and Persson, L.-E. (2006). Convex Functions and Their Applications, Springer.

2. Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for (𝒑, 𝕵)-convex fuzzy-interval-valued functions;Khan;AIMS Math.,2023

3. Khan, M.B., Othman, H.A., Voskoglou, M.G., Abdullah, L., and Alzubaidi, A.M. (2023). Some Certain Fuzzy Aumann Integral Inequalities for Generalized Convexity via Fuzzy Number Valued Mappings. Mathematics, 11.

4. Khan, M.B., Rakhmangulov, A., Aloraini, N., Noor, M.A., and Soliman, M.S. (2023). Generalized Harmonically Convex Fuzzy-Number-ValuedMappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities. Mathematics, 11.

5. Khan, M.B., Catas, A., Aloraini, N., and Soliman, M.S. (2023). Some Certain Fuzzy Fractional Inequalities for Up and Down ℏ-Pre-Invex via Fuzzy-Number Valued Mappings. Fractal Fract., 7.