In this paper we propose two different generalizations of the decomposition integral introduced by Even and Lehrer. We modify the product operator merging a given capacity and the decomposition coefficients by some more general functions F and G and compare properties of the obtained functionals with properties of the original decomposition integral. Generalized decomposition integrals corresponding to the particular decomposition systems, being generalizations of Shilkret, Choquet and concave integrals, are studied and exemplified.

中文翻译：

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广义分解积分

在本文中，我们提出了Even和Lehrer引入的分解积分的两种不同的概括。我们通过一些更通用的函数F和G修改合并给定容量和分解系数的乘积算子，并将获得的函数的性质与原始分解积分的性质进行比较。研究并举例说明了与特定分解系统相对应的广义分解积分，即Shilkret，Choquet和凹形积分的推广。