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Choquet-like integrals with respect to level-dependent capacities and \(\varphi \)-ordinal sums of aggregation function. (English) Zbl 1340.28020
Summary: In this study we merge the concepts of Choquet-like integrals and the Choquet integral with respect to level dependent capacities. For finite spaces and piece-wise constant level-dependent capacities our approach can be represented as a \(\varphi \)-ordinal sum of Choquet-like integrals acting on subdomains of the considered scale, and thus it can be regarded as extension method. The approach is illustrated by several examples.

28E10 Fuzzy measure theory
28E05 Nonstandard measure theory
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