Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of a-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper we present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utilit...

Keywords: Monotone measure Atom Weak null-additivity Regularity Sugeno integral Choquet integral a b s t r a c t In this paper, we prove some properties of atoms of weakly null-additive monotone measures. By using the regularity and weak null-additivity, a sin-gleton characterization of atoms of monotone measures on a metric space is shown. It is a generalization of previous results obtained by...

This paper introduces a novel approach to integrals with respect to capacities. Any random variable is decomposed as a combination of indicators. A prespecified set of collections of events indicates which decompositions are allowed and which are not. Each allowable decomposition has a value determined by the capacity. The decomposition-integral of a random variable is defined as the highest of...

This paper introduces a novel approach to integrals with respect to capacities. Any random variable is decomposed as a combination of indicators. A pre-speci ed set of collections of events indicates which decompositions are allowed and which are not. Each allowable decomposition has a value determined by the capacity. The decomposition-integral of a random variable is de ned as the highest of ...

It is well known that the main tool for finding dependencies among data is the linear regression model, which expresses one or several variables in term of a linear combination of the others. Linear regression is based on the least square principle, and has been studied at length, its statistical performance are well known. In real situations however, the linear assumption happens to be often r...

In decision under uncertainty, the Choquet integral yields the expectation of a random variable with respect to a fuzzy measure (or non-additive probability or capacity). In general, for the discrete setting, this technique allows to integrate functions taking values on a finite n-set with respect to a (fuzzy) measure taking values on subsets of such a set. Yet, the integrand may well be treate...

A model for a Choquet integral for arbitrary finite set systems is presented. The model includes in particular the classical model on the system of all subsets of a finite set. The general model associates canonical nonnegative and positively homogeneous superadditive functionals with generalized belief functions relative to an ordered system, which are then extended to arbitrary valuations on ...

Establishing a good algorithm for predicting temperature of thermostable proteins is an important issue. In this study, a new thermostable proteins prediction method by using Hurst exponent and Choquet integral regression model with respect to maximized L-measure is proposed. The main idea of this method is to integrate the physicochemical properties, long term memory property and Choquet integ...