Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for (p, J)-convex fuzzy-interval-valued functions

Khan M. B., Santos-Garcia G., Budak H., Treanta S., Soliman M. S.

AIMS MATHEMATICS, no.3, pp.7437-7470, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.3934/math.2023374
  • Journal Name: AIMS MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.7437-7470
  • Kocaeli University Affiliated: No

Abstract

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.