d-Choquet integrals: Choquet integrals based on dissimilarities

The paper introduces a new class of functions from [0, 1](n) to [0, n] called d-Choquet integrals. These functions are a generalization of the standard Choquet integral obtained by replacing the difference in the definition of the usual Choquet integral by a dissimilarity function. In particular, the class of all d-Choquet integrals encompasses the class of all standard Choquet integrals but the use of dissimilarities provides higher flexibility and generality. We show that some d-Choquet integrals are aggregation/preaggregation/averaging/functions and some of them are not. The conditions under which this happens are stated and other properties of the d-Choquet integrals are studied. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

The paper introduces a new class of functions called d-Choquet integrals, which are a generalization of the standard Choquet integral by replacing the difference in the definition with a dissimilarity function. Some d-Choquet integrals are aggregation functions, while others are not, and the conditions for this are explored in the study of their properties.