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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.

MSC:
28E10 Fuzzy measure theory
28E05 Nonstandard measure theory
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