Abstract In this paper, we present the concepts of generalized derivative, directional generalized derivative, subdifferential and conjugate for n-dimensional fuzzy-number-valued functions and discuss the characterizations of generalized derivative and directional generalized derivative by, respectively, using the derivative and directional derivative of crisp functions that are determined by the fuzzy mapping. Furthermore, the relations among generalized derivative, directional generalized derivative, subdifferential and convexity for n-dimensional fuzzy-number-valued functions are investigated. Finally, under two kinds of partial orderings defined on the set of all n-dimensional fuzzy numbers, the duality theorems and saddle point optimality criteria in fuzzy optimization problems with constraints are discussed.

中文翻译：

---

n维模糊数值函数的广义导数和优化问题

摘要 本文提出了n维模糊数值函数的广义导数、方向广义导数、次微分和共轭的概念，并分别利用导数和方向广义导数讨论了广义导数和方向广义导数的表征。由模糊映射确定的清晰函数的导数。进一步研究了n维模糊数值函数的广义导数、方向广义导数、次微分和凸性之间的关系。最后，在所有n维模糊数集上定义的两种偏序下，讨论了带约束模糊优化问题中的对偶定理和鞍点最优准则。