Some New Estimates of Fuzzy Integral Inequalities for Harmonically Convex Fuzzy-Number-Valued Mappings via up and down Fuzzy Relation

Abstract

In this article, the up and down harmonically convex fuzzy-number-valued mapping which is a novel kind of harmonically convex fuzzy-number-valued mapping is introduced. In addition, it is highlighted that the new idea of up and down harmonically convex fuzzy-number-valued mapping (U−O−H convex F−N−V−M), which is a generalization of the previous class, describes a variety of new and classical classes as special cases by employing some mild restrictions. With the help of fuzzy inclusion relation, the new versions of the Hermite–Hadamard-type (HH-type) inequalities for up and down harmonically convex fuzzy-number-valued mappings are established. Then, we introduce a new version of Hermite–Hadamard Fejér-type inequality via fuzzy inclusion relation by using up and down harmonically convex fuzzy-number-valued mapping. Additionally, several instances are given to illustrate our main findings.