Authors: Salvatore Greco (Faculty of Economics, University of Catania), Benedetto Matarazzo and Silvio Giove (Faculty of Economics, University of Venice)
Area: Decision Theory
In many decision problems a set of alternatives is evaluated with respect to a set of points of view, called criteria. For
example, in evaluating a car one can consider criteria such as maximum speed, price, acceleration, fuel consumption.
In general, evaluations of an alternative with respect to different
criteria can be conflicting with respect to preferences. For example, very often when a car has a good maximum speed,
it has also a high price and a high fuel consumption. Thus, in order to express a decision it is necessary to aggregate
the evaluations on considered criteria. This is the domain of multiple criteria decision
analysis and in this context several methodologies have been proposed.
One of the simplest aggregation procedures is the weighted sum of the evaluations with respect to considered
criteria. Some more complex aggregation procedures have been proposed in order to take into account specific aspects
in evaluating importance of criteria, such as interaction among criteria, which has been considered through nonadditive
integrals, such as Choquet integral and Sugeno integral.
In this talk we present a generalization of Choquet integral in which the capacity depends also on the value of the aggregated variables.
We show that as particular cases of our generalization of Choquet integral there are the Sugeno integral, the Šipoš integral and the Cumulative Prospect Theory functional.