## 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:

 2.8e+11 Fuzzy measure theory 3e+72 Theory of fuzzy sets, etc.
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### References:

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