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Choquet-like integrals with respect to level-dependent capacities and ϕ -ordinal sums of aggregation function

Radko Mesiar, Peter Smrek (2015)

Kybernetika

In this study we merge the concepts of Choquet-like integrals and the Choquet integral with respect to level dependent capacities. For finite spaces and piece-wise constant level-dependent capacities our approach can be represented as a ϕ -ordinal sum of Choquet-like integrals acting on subdomains of the considered scale, and thus it can be regarded as extension method. The approach is illustrated by several examples.

Classes of fuzzy measures and distortion

Ľubica Valášková, Peter Struk (2005)

Kybernetika

Distortion of fuzzy measures is discussed. A special attention is paid to the preservation of submodularity and supermodularity, belief and plausibility. Full characterization of distortion functions preserving the mentioned properties of fuzzy measures is given.

Conditional states and joint distributions on MV-algebras

Martin Kalina, Oľga Nánásiová (2006)

Kybernetika

In this paper we construct conditional states on semi-simple MV-algebras. We show that these conditional states are not given uniquely. By using them we construct the joint probability distributions and discuss the properties of these distributions. We show that the independence is not symmetric.

Construction of aggregation operators: new composition method

Tomasa Calvo, Andrea Mesiarová, Ľubica Valášková (2003)

Kybernetika

A new construction method for aggregation operators based on a composition of aggregation operators is proposed. Several general properties of this construction method are recalled. Further, several special cases are discussed. It is also shown, that this construction generalizes a recently introduced twofold integral, which is exactly a composition of the Choquet and Sugeno integral by means of a min operator.

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