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arXiv · 2105.11138

On balanced capacities

Taras Radul
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Abstract

We consider capacity (fuzzy measure, non-additive probability) on a compactum as a monotone cooperative normed game. Then it is naturally to consider probability measures as elements of core of such game. We prove an analogue of Bondareva-Shapley theorem that non-emptiness of the core is equivalent to balancedness of the capacity. We investigate categorical properties of balanced capacities and give characterizations of some fuzzy integrals of balanced capacities.

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Taras Radul. 2021-05-24. On balanced capacities. https://arxiv.org/abs/2105.11138

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