Abstract In this paper we will prove that the nearest trapezoidal approximation of fuzzy numbers with respect to weighted L 2 -type metrics with or without additional constraints can be obtained via quadratic programs. Actually, the approach is even more general based on so called finite polyhedral subsets of fuzzy numbers which include most of the important special classes of fuzzy numbers available in the literature. In particular, we will recapture the algorithm to compute the nearest weighted trapezoidal approximation of a fuzzy number by a method which we believe that has the potential to be extended to more complex approximation problems. Then, we will improve the Lipschitz constant of the trapezoidal approximation operator preserving the ambiguity. To achieve this improved result we will exploit the fact that we have an analytical expression for this operator. However, note that the same result is obtained if this solution function is described by quadratic programs. Therefore, for similar problems we still can obtain Lipschitz constants for the approximation operator even if an analytical expression of this operator is not available.

中文翻译：

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使用二次规划的模糊数的梯形逼近

摘要 在本文中，我们将证明关于带或不带附加约束的加权 L 2 型度量的模糊数的最近梯形近似可以通过二次规划获得。实际上，该方法基于所谓的模糊数的有限多面体子集更加通用，其中包括文献中可用的大多数重要的特殊模糊数类别。特别是，我们将通过一种我们认为有可能扩展到更复杂的逼近问题的方法来重新捕获计算模糊数的最近加权梯形逼近的算法。然后，我们将改进梯形近似算子的 Lipschitz 常数，同时保留歧义。为了实现这个改进的结果，我们将利用我们有这个运算符的解析表达式这一事实。但是，请注意，如果此解函数由二次程序描述，将获得相同的结果。因此，对于类似的问题，我们仍然可以获得近似算子的 Lipschitz 常数，即使该算子的解析表达式不可用。