Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan.
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada.
Math Biosci Eng. 2022 Jan;19(1):812-835. doi: 10.3934/mbe.2022037. Epub 2021 Nov 22.
In this paper, firstly we define the concept of -preinvex fuzzy-interval-valued functions (-preinvex FIVF). Secondly, some new Hermite-Hadamard type inequalities (- type inequalities) for -preinvex FIVFs via fuzzy integrals are established by means of fuzzy order relation. Finally, we obtain Hermite-Hadamard Fejér type inequalities (- Fejér type inequalities) for -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.
本文首先定义了 - 预不变模糊区间值函数（-preinvex FIVF）的概念。其次，利用模糊序关系，通过模糊积分建立了一类新的 - 预不变模糊区间值函数的 Hermite-Hadamard 型不等式（- 型不等式）。最后，利用上述关系得到了 - 预不变模糊区间值函数的 Hermite-Hadamard Fejér 型不等式（- Fejér 型不等式）。为了加强我们的结果，我们提供了一些例子来说明我们结果的有效性，并得到了一些新的和以前已知的结果。
