Some new versions of integral inequalities for log-preinvex fuzzy-interval-valued functions through fuzzy order relation

In this paper, firstly we define the new class of log-preinvex fuzzy-interval-valued functions which is called log-h-preinvex fuzzy-interval-valued functions (log-h-preinvex FIVFs) by means of fuzzy order relation. This fuzzy order relation is defined level wise through Kulisch-Miranker order relation defined on fuzzy-interval space. Secondly, some new Hermite-Hadamard-type and Hermite-Hadamard-Fejér inequalities for log-h-preinvex FIVFs via fuzzy integrals are also established. Finally, we obtain some related inequalities for log-h-preinvex FIVFs. To strengthen our results, we provide some examples to illustrate the validation of our results, and several new and previously known results are obtained.