Abstract
It is a well-known fact that convex and non-convex fuzzy mappings play a critical role in the study of fuzzy optimization. Due to the behavior of its definition, the idea of convexity also plays a significant role in the subject of inequalities. The concepts of convexity and symmetry have a tight connection. We may use whatever we learn from both the concepts, owing to the significant correlation that has developed between both in recent years. In this paper, we introduce a new class of harmonically convex fuzzy-interval-valued functions which is known as harmonically h-convex fuzzy-interval-valued functions (abbreviated as harmonically h-convex F-I-V-Fs) by means of fuzzy order relation. This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation defined on interval space. Some properties of this class are investigated. BY using fuzzy order relation and h-convex F-I-V-Fs, Hermite–Hadamard type inequalities for harmonically are developed via fuzzy Riemann integral. We have also obtained some new inequalities for the product of harmonically h-convex F-I-V-Fs. Moreover, we establish Hermite–Hadamard–Fej’er inequality for harmonically h-convex F-I-V-Fs via fuzzy Riemann integral. These outcomes are a generalization of a number of previously known results, as well as many new outcomes can be deduced as a result of appropriate parameter “θ” and real valued function “∇” selections. For the validation of the main results, we have added some nontrivial examples. We hope that the concepts and techniques of this study may open new directions for research.
Highlights
Convex analysis has contributed significantly to the advancement of applied and pure research
Several inequalities have been proposed as convex function applications
We refer the readers for further analysis to literature on the applications and properties of fuzzy-interval, and inequalities and generalized convex fuzzy mappings, see [33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53] and the references therein
Summary
Convex analysis has contributed significantly to the advancement of applied and pure research. Several inequalities have been proposed as convex function applications. Kamran et al [26] developed the H · H inequality by means of the notion of interval-valued generalized p-convex functions. We refer the readers for further analysis to literature on the applications and properties of fuzzy-interval, and inequalities and generalized convex fuzzy mappings, see [33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53] and the references therein. We have discussed some new and classical inequalities as exceptional cases
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