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On nearly radial marginals of high-dimensional probability measures

Bo'az Klartag (2010)

Journal of the European Mathematical Society

Suppose that μ is an absolutely continuous probability measure on R n, for large n . Then μ has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if n ( C / ε ) C d , then there exist d -dimensional marginals of μ that are ε -far from being sphericallysymmetric, in an appropriate sense. Here C > 0 is a universal constant.

p -symmetric bi-capacities

Pedro Miranda, Michel Grabisch (2004)

Kybernetika

Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order 3 n , instead of 2 n for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of p -symmetric bi- capacities, in the same spirit as for p -symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature,...

Twofold integral and multi-step Choquet integral

Yasuo Narukawa, Vicenç Torra (2004)

Kybernetika

In this work we study some properties of the twofold integral and, in particular, its relation with the 2-step Choquet integral. First, we prove that the Sugeno integral can be represented as a 2-step Choquet integral. Then, we turn into the twofold integral studying some of its properties, establishing relationships between this integral and the Choquet and Sugeno ones and proving that it can be represented in terms of 2-step Choquet integral.

Why λ -additive (fuzzy) measures?

Ion Chiţescu (2015)

Kybernetika

The paper is concerned with generalized (i. e. monotone and possibly non-additive) measures. A discussion concerning the classification of these measures, according to the type and amount of non-additivity, is done. It is proved that λ -additive measures appear naturally as solutions of functional equations generated by the idea of (possible) non additivity.

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