An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure.

*(English)*Zbl 0662.28015In 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.

##### Keywords:

non-additivity of Sugeno’s fuzzy measure; Choquet integral; representation of a fuzzy measure
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\textit{T. Murofushi} and \textit{M. Sugeno}, Fuzzy Sets Syst. 29, No. 2, 201--227 (1989; Zbl 0662.28015)

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##### References:

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