New Hermite–Hadamard and Jensen inequalities for log-$$s$$-convex fuzzy-interval-valued functions in the second sense
Пэйдэ Лю, Muhammad Bilal Khan, Muhammad Aslam Noor, Khalida Inayat Noor
Abstract
Abstract In this paper, our aim is to consider the new class of log-convex fuzzy-interval-valued function known as log- s -convex fuzzy-interval-valued functions (log- s -convex fuzzy-IVFs). By this concept, we have introduced Hermite–Hadamard inequalities (HH-inequalities) by means of fuzzy order relation. This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation defined on interval space. Moreover, some new Hermite–Hadamard–Fejér inequalities (HH–Fejér-inequalities) and Jensen’s inequalities via log- s -convex fuzzy-IVFs are also established and verified with the support of useful examples. Some special cases are also discussed which can be viewed as applications of fuzzy-interval HH-inequalities. The concepts and approaches of this paper may be the starting point for further research in this area.