After giving a calculation formula for the g-derivative for a fuzzy-valued function with unilateral derivatives of the endpoint functions of level sets and characterizing the partial order relations between two fuzzy intervals by their generalized difference, we present the optimality conditions of weak LU-minimum solutions for fuzzy optimization problems by using the partial generalized differentiability and directional generalized differentiability. The optimization conditions obtained in this article extend the results in the literature. Examples are also given to illustrate the main theorems.

中文翻译：

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广义可微下多变量模糊优化的最优条件

给出了水平集端点函数单边导数的模糊值函数的g-导数的计算公式，并通过它们的广义差表征了两个模糊区间之间的偏序关系，给出了弱LU-的最优性条件。使用偏广义可微性和方向广义可微性的模糊优化问题的最小解。本文获得的优化条件扩展了文献中的结果。还给出了例子来说明主要定理。