The ranking of fuzzy numbers has an important position in fuzzy application models and systems. In this paper, a two-dimensional approach is proposed by the Monte Carlo simulation technique, and the simulation formula of the possibility degree is established. The algorithms for ranking interval numbers, triangular fuzzy numbers and trapezoidal fuzzy numbers are elaborated on. Moreover, the axiomatic properties of the possibility degree formulae are investigated. It is found that the simulation formula of the possibility degree is reasonable for the satisfaction of the considered axiomatic properties. Finally, by considering a set of fuzzy numbers and the effect of a viewpoint, some comparisons are reported by carrying out numerical examples. The observations reveal that the proposed simulation method is effective to reflect the uncertainty of fuzzy numbers and coherent with the human intuition.

中文翻译：

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一种利用蒙特卡罗技术对模糊数进行排序的二维模拟方法

模糊数的排序在模糊应用模型和系统中具有重要地位。本文利用蒙特卡罗模拟技术提出了一种二维方法，建立了可能性度的模拟公式。详细阐述了区间数、三角模糊数和梯形模糊数的排序算法。此外，研究了可能性度公式的公理性质。发现可能性度的模拟公式对于所考虑的公理性质的满足是合理的。最后，通过考虑一组模糊数和一个视点的影响，通过数值例子报告了一些比较。