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**Choquet integral and fuzzy measures on locally compact space.**
*(English)*
Zbl 0977.28012

Summary: The concept of outer regular fuzzy measures is proposed, and it is shown that a functional of certain type on the cone of positive continuous functions with compact supports is represented as a Choquet integral with respect to an outer regular fuzzy measure. It is also shown that the Choquet integral of positive continuous functions with compact supports is represented as a Lebesgue integral with the same integrands. This representation is a generalization of certain previous results of others, which are useful for computation of the upper and lower expected value.

### MSC:

28E10 | Fuzzy measure theory |

28C99 | Set functions and measures on spaces with additional structure |

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\textit{M. Sugeno} et al., Fuzzy Sets Syst. 99, No. 2, 205--211 (1998; Zbl 0977.28012)

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### References:

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