The concept of null set in the space of fuzzy numbers is introduced. Based on this concept, we can define two partial orderings according to the subtraction and Hukuhara difference between any two fuzzy numbers. These two partial orderings will be used to define the solution concepts of fuzzy optimization problems. On the other hand, we transform the fuzzy optimization problems into a conventional vector optimization problem. Under these settings, we can apply the technique of scalarization to solve this transformed vector optimization problem. Finally, we show that the optimal solution of the scalarized problem is also the optimal solution of the original fuzzy optimization problem.

中文翻译：

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应用空集的概念解决模糊优化问题

介绍了模糊数空间中空集的概念。基于此概念，我们可以根据任意两个模糊数之间的减法和Hukuhara差异来定义两个偏序。这两个部分排序将用于定义模糊优化问题的解决方案概念。另一方面，我们将模糊优化问题转化为常规的矢量优化问题。在这些设置下，我们可以应用标量化技术来解决此转换向量优化问题。最后，我们证明了标量问题的最优解也是原始模糊优化问题的最优解。