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    Generalized p-Convex Fuzzy-Interval-Valued Functions and Inequalities Based upon the Fuzzy-Order Relation
    (Mdpi, 2022) Khan, Muhammad Bilal; Treanta, Savin; Budak, Hüseyin
    Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called (p,s)-convex fuzzy interval-valued functions ((p,s)-convex F-I-V-Fs) in the second sense and to establish Hermite-Hadamard (H-H) type inequalities for (p,s)-convex F-I-V-Fs using fuzzy order relation. In addition, we demonstrate that our results include a large class of new and known inequalities for (p,s)-convex F-I-V-Fs and their variant forms as special instances. Furthermore, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions.
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    Some new versions of jensen, schur and hermite-hadamard type inequalities for (P,j)-convex fuzzy-interval-valued functions
    (American Institute of Mathematical Sciences, 2023) Khan, Muhammad Bilal; Santos-García, G.; Budak, Hüseyin; Treanta, Savin; Soliman, M.S.
    To create various kinds of inequalities, the idea of convexity is essential. Convexity and integral inequality hence have a significant link. This study's goals are to introduce a new class of generalized convex fuzzy-interval-valued functions (convex FIVFs) which are known as (p,J) -convex FIVFs and to establish Jensen, Schur and Hermite-Hadamard type inequalities for (p,J) -convex FIVFs using fuzzy order relation. The Kulisch-Miranker order relation, which is based on interval space, is used to define this fuzzy order relation level-wise. Additionally, we have demonstrated that, as special examples, our conclusions encompass a sizable class of both new and well-known inequalities for (p,J) -convex FIVFs. We offer helpful examples that demonstrate the theory created in this study's application. These findings and various methods might point the way in new directions for modeling, interval-valued functions and fuzzy optimization issues. © 2023, American Institute of Mathematical Sciences. All rights reserved.