Quadrature-Inspired Generalized Choquet Integral

In this study, we present an innovative approach to deriving an aggregate classification score based on multiple classifiers based on generalizations of the Choquet integral. These generalizations are inspired by the quadratures known from numerical analysis, used to calculate integrals, e.g. the Newton-Cotes formula. The previous formulas for calculating generalizations of the Choquet integral used two (e.g. the case of the difference of these values), or three adjacent values related to the degrees of belonging of a given element to individual classes, related to one density of the fuzzy measure. In this article, we offer an interesting generalization. The novel enhancement is based on the replacement of typical product or t-norm appearing under the integral sign by forms related to mathematical quadratures. The formulas become more precise and better reflect the idea of integration. Moreover, a series of numerical experiments confirmed the advantage of the new approach over the existing ones.