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On the Choquet integral for Riesz space valued measure. (English) Zbl 0992.46036
The Choquet integral for a real function with respect to a complete Riesz space valued fuzzy measure is defined and the Choquet integral is equal to the Lebesgue integral in the case \(\sigma \)-additivity of fuzzy measure is proved. As applications there are presented: the constructions of vector valued belief and plausibility measures, the formulation of the Wierman extension principle, and the Möbius transform for vector valued measure.

MSC:
46G10 Vector-valued measures and integration
46A40 Ordered topological linear spaces, vector lattices
28B15 Set functions, measures and integrals with values in ordered spaces
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