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An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure. (English) Zbl 0662.28015
In this paper the non-additivity of Sugeno’s fuzzy measure is interpreted in terms of addition and the rationality of the Choquet integral is discussed. It is pointed out that a fuzzy measure on a set X expresses the interaction between the subsets of X and can be represented by an additive measure. It is shown through concrete examples that the Choquet integral is reasonable as an integral with respect to a fuzzy measure. It is also found that the Choquet integral is closely related with the representation of a fuzzy measure.

MSC:
28E10 Fuzzy measure theory
03E72 Theory of fuzzy sets, etc.
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