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.
n this paper we study the set of copulas for which both a horizontal section and a vertical section have been given. We give a general construction for copulas of this type and we provide the lower and upper copulas with these sections. Symmetric copulas with given horizontal section are also discussed, as well as copulas defined on a grid of the unit square. Several examples are presented.
Based on a recent representation of copulas invariant under univariate conditioning, a new class of copulas linked to a distortion of the identity function is introduced and studied.
In this paper further development of Chebyshev type inequalities for Sugeno integrals based on an aggregation function H and a scale transformation φ is given. Consequences for T-(S-)evaluators are established.
This paper deals with the concept of the "size" or "extent" of the information in the sense of measuring the improvement of our knowledge after obtaining a message. Standard approaches are based on the probabilistic parameters of the considered information source. Here we deal with situations when the unknown probabilities are subjectively or vaguely estimated. For the considered fuzzy quantities valued probabilities we introduce and discuss information theoretical concepts.
The aim of this paper is to open a new way of modelling non-exchangeable random variables with a class of Archimax copulas. We investigate a connection between powers of generators and dependence functions, and propose some construction methods for dependence functions. Application to different hydrological data is given.