Interval type-2 fuzzy sets provide us with additional degrees of freedom to represent the uncertainty and the fuzziness of the real word than traditional type-1 fuzzy sets. Interval type-2 fuzzy numbers ranking has an important role in the decision making analysis. In this paper, the probatilistic mean value and variance of interval type-2 fuzzy numbers are proposed based on the Mellin transform for type-1 fuzzy numbers. The interval type-2 fuzzy number with the higher mean is ranked higher. If the mean values are equal the one with the smaller variance is judged higher rank. On this basis, some new distance measures and possibility degree formula are proposed to comparing interval type-2 fuzzy numbers based on their Mellin mean value and variance. Some benchmarking numerical examples are given, and some interpretation issues are explained.

中文翻译：

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基于梅林变换的区间二型模糊数排序新方法

区间 2 型模糊集比传统的 1 型模糊集为我们提供了额外的自由度来表示真实词的不确定性和模糊性。区间二型模糊数排序在决策分析中具有重要作用。本文基于一类模糊数的梅林变换，提出了区间二类模糊数的概率均值和方差。具有较高均值的区间类型 2 模糊数排名较高。如果平均值相等，则方差较小的那个被判断为较高的等级。在此基础上，提出了一些新的距离测度和可能性度公式来比较基于Mellin均值和方差的区间2型模糊数。给出了一些基准数值示例，并解释了一些解释问题。