Abstract The paper introduces a new class of functions from [ 0 , 1 ] n to [ 0 , n ] called d-Choquet integrals. These functions are a generalization of the “standard” Choquet integral obtained by replacing the difference in the definition of the usual Choquet integral by a dissimilarity function. In particular, the class of all d-Choquet integrals encompasses the class of all “standard” Choquet integrals but the use of dissimilarities provides higher flexibility and generality. We show that some d-Choquet integrals are aggregation/pre-aggregation/averaging/functions and some of them are not. The conditions under which this happens are stated and other properties of the d-Choquet integrals are studied.

中文翻译：

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d-Choquet 积分：基于相异性的 Choquet 积分

摘要 本文介绍了一类从 [ 0 , 1 ] n 到 [ 0 , n ] 的新函数，称为 d-Choquet 积分。这些函数是“标准”Choquet 积分的推广，通过用相异函数替换通常 Choquet 积分定义中的差异而获得。特别是，所有 d-Choquet 积分的类包含所有“标准”Choquet 积分的类，但使用相异性提供了更高的灵活性和通用性。我们表明，一些 d-Choquet 积分是聚合/预聚合/平均/函数，而其中一些不是。说明了发生这种情况的条件，并研究了 d-Choquet 积分的其他性质。