A generalization of the discrete Choquet and Sugeno integrals based on a fusion function

Abstract

In this paper, we present an approach to generalization of the discrete Choquet and Sugeno integrals. For the Choquet integral we replace the product operator joining the values of a capacity m of criteria sets and values of a score vector by a fusion function F satisfying some constraints, similarly as was already done for another form of the discrete Choquet integral by Mesiar et al. in [15]. For the Sugeno integral we use an analogous method of generalization replacing the minimum operator by a fusion function. The properties of the obtained functionals CFm and SFm are studied and some examples for particular capacity m and particular fusion function F are given.