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

Muhammad Bilal Khan, Ali Althobaiti, Cheng-Chi Lee (), Mohamed S. Soliman and Chun-Ta Li ()
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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
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

Mathematics, 2023, vol. 11, issue 13, 1-23

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.

Keywords: fuzzy-interval-valued function on coordinates; coordinated up and down convex fuzzy-number-valued mapping; fuzzy double integral; Hermite–Hadamard–Fejér-type inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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