We study the notion of conditional relative importance in a quantitative framework. This is an important notion in the context of the Choquet integral since this latter is usually motivated by this decisional behavior. A systematic investigation on generalizations of the Choquet integral is performed. The determination of the utility function is central in this analysis.

In this paper we discuss the Choquet integral model in the realm of Preference Learning, and point out advantages of learning simultaneously partial utility functions and capacities rather than sequentially, i.e., first utility functions and then capacities or vice-versa. Moreover, we present possible interpretations of the Choquet integral model in Preference Learning based on Shapley values a...

In this paper we study the extension of Choquet integrals to ordinal scales. We show that two different integrals can be defined on the basis of two different but equivalent expressions in the numerical case. We prove some properties of the Choquet integrals and show their application to aggregation.

We show that the Choquet integral is the unique linear interpolator between vertices of the [0, 1] hypercube, using the least possible number of vertices. Related results by Lovász and Singer are discussed, as well as other interpolations. We show that the Choquet integral for bi-capacities can be also casted into this framework. Lastly, we discuss the case of Sugeno integral.

Rock physics models are widely used in hydrocarbon reservoir studies. These models make it possible to simulate a reservoir more accurately and reduce the economic risk of oil and gas exploration. In the current study, two models of Self-Consistent Approximation followed by Gassmann (SCA-G) and Xu-Payne (X-P) were implemented on three wells of a carbonate reservoir in the southwest of Ira...

The concept of universal integral, recently proposed, generalizes the Choquet, Shilkret and Sugeno integrals. Those integrals admit a bipolar formulation, useful in those situations where the underlying scale is bipolar. In this paper we propose the bipolar universal integral generalizing the Choquet, Shilkret and Sugeno bipolar integrals. To complete the generalization we also provide the char...

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...