In this paper, the definitions of Clarke generalized directional \(\alpha \) -derivative and Clarke generalized gradient are introduced for a locally Lipschitz fuzzy function. Further, a nonconvex nonsmooth optimization problem with fuzzy objective function and both inequality and equality constraints is considered. The Karush-Kuhn-Tucker optimality conditions are established for such a nonsmooth extremum problem. For proving these conditions, the approach is used in which, for the considered nonsmooth fuzzy optimization problem, its associated bi-objective optimization problem is constructed. The bi-objective optimization problem is solved by its associated scalarized problem constructed in the weighting method. Then, under invexity hypotheses, (weakly) nondominated solutions in the considered nonsmooth fuzzy minimization problem are characterized through Pareto solutions in its associated bi-objective optimization problem and Karush-Kuhn-Tucker points of the weighting problem.

在本文中，克拉克的定义广义有向\(\alpha\)为局部 Lipschitz 模糊函数引入了导数和 Clarke 广义梯度。此外，考虑了具有模糊目标函数和不等式和等式约束的非凸非光滑优化问题。为这样的非光滑极值问题建立了 Karush-Kuhn-Tucker 最优条件。为了证明这些条件，使用这种方法，对于所考虑的非光滑模糊优化问题，构造其相关的双目标优化问题。双目标优化问题通过其在加权方法中构造的相关标量化问题来解决。然后，在 invexity 假设下，