@article{Khan2023, 
author = {Muhammad Bilal Khan and Gustavo Santos-García and Hüseyin Budak and Savin Treanțǎ and Mohamed S. Soliman},
title = {Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for        (                  p            ,              J              )  -convex fuzzy-interval-valued functions},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {7437-7470},
keywords = {Hermite-Hadamard type inequality, Jensen type inequality, fuzzy Riemann integral, (p, J)-convex fuzzy-interval-valued function, Schur type inequality, Hermite-Hadamard-Fejér type inequality},
url = {https://www.sciopen.com/article/10.3934/math.2023374},
doi = {10.3934/math.2023374},
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.}
}