In a recent work, we proposed a generalization of logistic regression based on the Choquet integral. Our approach, referred to as choquistic regression, makes it possible to capture non-linear dependencies and interactions among predictor variables while preserving two important properties of logistic regression, namely the comprehensibility of the model and the possibility to ensure its monoto...

Motivated by the recent results on topology determined by the Sugeno and Choquet integrals we study the topology on the space of measurable functions for a non-additive measure, which is determined by the integral IS based on a semicopula S. We define a family of mappings ρS on the set of measurable functions parameterized by a semicopula S and study their properties. We show that for a semicop...

In this paper, the Choquet integral and the interval neutrosophic set theory are combined to make multi-criteria decision for problems under neutrosophic fuzzy environment. Firstly, a ranking index is proposed according to its geometrical structure, and an approach for comparing two interval neutrosophic numbers is given. Then, a ≤L implied operation-invariant total order which satisfies order-...

Several discrete universal integrals on finite universes are discussed from an axiomatic point of view. We start from the first attempt due to B. Riemann and cover also most recent approaches based on level dependent capacities. Our survey includes, among others, the Choquet and the Sugeno integral and general copula-based integrals.

This paper briefly presents the evolutions of the ordered sorting procedure TOMASO based on the Choquet integral as a discriminant function. The method uses information provided by the Decision Maker (DM) in terms of a set of prototypes (alternatives well-known to the DM). This questioning is restricted to his expertise domain and not to technical parameters linked to the method. The method wor...

Parameter adjustment of a fusion system for 3D image interpretation is often a difficult task that is emphasized by the non understandability of the parameters by the end-users. Moreover, such fusion systems are complex because they involve a complete information treatment chain (from the information extraction to the decision). The sub-parts of the system concern also different scientific area...

We investigate the distribution functions and the moments of the so-called Choquet integral, also known as the Lovász extension, when regarded as a real function of a random sample drawn from a continuous population. Since the Choquet integral includes weighted arithmetic means, ordered weighted averaging operators, and lattice polynomials as particular cases, our results encompass the correspo...

The idea of using the Choquet integral as an aggregation operator in machine learning has gained increasing attention in recent years, and a number of corresponding methods have already been proposed. Complementing these contributions from a more theoretical perspective, this paper addresses the following question: What is the VC dimension of the (discrete) Choquet integral when being used as a...

In this paper, we review two of the most well-known citation indexes and establish their connections with the Choquet and Sugeno integrals. In particular, we show that the recently established -index is a particular case of the Sugeno integral, and that the number of citations corresponds to the Choquet integral. In both cases, they use the same fuzzy measure. The results presented here permit ...

Based on the Choquet integral and the generalized Shapley function, two new induced Atanassov’s interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov’s interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov’s interval-val...