Bi-capacities arise as a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wide variety of decision behaviours, encompassing models as Cumulative Prospect Theory (CPT). The aim of this paper in two parts is to present the machinery behind bicapacities, and thus remains on a rather theoretical ...

In this paper we study decision making models based on aggregation operators and, more specially, on Choquet integrals. The motivation of our work is to study the modeling capabilities of these operators and to build models that can approximate arbitrary functions. We describe and study two models that are universal approximators.

The current approaches to construct a multi-criteria model based on a Choquet integral are split into two separate steps: construct first the utility functions and then the aggregation function. Unfortunately, the decision maker may feel some difficulties in addressing these tricky steps. In this paper, we propose a preference learning algorithm that constructs both the utility functions and th...

Anew integral for capacities is introduced and characterized. It differs from the Choquet integral on non-convex capacities. The main feature of the new integral is concavity, whichmight be interpreted as uncertainty aversion. The integral is extended to fuzzy capacities, which assign subjective expected values to random variables (e.g., portfolios) and may assign subjective probability only to...

Fuzzy measures (FMs) encode the worth (or importance) of different subsets of information sources in the fuzzy integral (FI). It is well-known that the Choquet FI (CFI) often reduces to an elementary aggregation operator for different selections of the FM. However, FMs are often learned from training data or they are derived from the densities (worth of just the singletons). In these situations...

The paper deals with a recently proposed approach to combining classifiers by means of fuzzy aggregation. The approach relies on the quasi-Sugeno integral and on the t-conorm integral as a generalization of the Choquet and Sugeno integral, which have been used for combining classifiers so far. New theoretical development is presented, in particular a proposition concerning the λ measures used i...