Abstract We analyze the probabilistic features of the Choquet integral with respect to a capacity where the inputs are random variables. Only a few papers deal with this issue. We give two different formulas for the density function of the output when the input variables are independent and identically distributed random variables. We also calculate the first moment of the Choquet integral, and we compare our results with the ones obtained in the literature which mainly concerns the cases where the common distribution of the input variables is either uniform or exponential.

中文翻译：

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Choquet 积分与随机条目

摘要 我们分析了 Choquet 积分相对于输入是随机变量的容量的概率特征。只有少数论文涉及这个问题。当输入变量是独立同分布的随机变量时，我们给出两种不同的输出密度函数公式。我们还计算了 Choquet 积分的一阶矩，并将我们的结果与文献中获得的结果进行比较，文献中主要涉及输入变量的公共分布是均匀分布或指数分布的情况。