In this paper, firstly we define the concept of h-preinvex fuzzy-interval-valued functions (h-preinvex FIVF). Secondly, some new Hermite-Hadamard type inequalities (H-H type inequalities) for h-preinvex FIVFs via fuzzy integrals are established by means of fuzzy order relation. Finally, we obtain Hermite-Hadamard Fejér type inequalities (H-H Fejér type inequalities) for h-preinvex FIVFs by using above relationship. To strengthen our result, we provide some examples to illustrate the validation of our results, and several new and previously known results are obtained.
Keywords: fuzzy integral; fuzzy-interval Hermite-Hadamard type inequalities; fuzzy-interval Hermite-Hadamard-Fejér inequalities; h-preinvex fuzzy-interval-valued functions.