We introduce bi-capacities as a natural generalization of capacities (or fuzzy measures) through the identity of Choquet integral of binary alternatives with fuzzy measures. We examine the underlying structure and derive the Möbius transform of bi-capacities. Next, the Choquet and Sugeno integrals w.r.t bicapacities are introduced. It is shown that symmetric and asymmetric integrals are recover...

In the context of multicriteria decision making whose aggregation process is based on the Choquet integral, bi-capacities can be regarded as a natural extension of capacities when the underlying evaluation scale is bipolar. The notion of entropy, recently generalized to capacities to measure their uniformity, is now extended to bi-capacities. We show that the resulting entropy measure has a ver...

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...

A Sugeno and a Choquet integrals are commonly used fuzzy integrals for aggregation. As a generalization of both integrals, the twofold integral is induced. The twofold integral enables us to interpret two measures from a different semantics viewpoint. One corresponds to the Choquet integral and the other corresponds to the Sugeno integral. Our work is about building models for the twofold integ...

We analyze the probabilistic features of Choquet integral with respect to a capacity where inputs are random variables. Only few papers deal this issue. give two different formulas for density function output when input variables independent and identically distributed also calculate first moment integral, we compare our results ones obtained in literature which mainly concerns cases common dis...

Expectation is the fundamental concept in statistics and probability. As two generalizations of expectation, Choquet and Choquet-like expectations are commonly used tools in generalized probability theory. This paper considers the Stolarsky inequality for two classes of Choquet-like integrals. The first class generalizes the Choquet expectation and the second class is an extension of the Sugeno...