Analysis of smooth and enhanced smooth quadrature-inspired generalized Choquet integral

Abstract

Enhancing the ability to make informed decisions stands as a significant challenge in modern IT. Specifically, there is a growing need to improve the efficiency of classification algorithms. When faced with multiple results derived from various methods, one can select the most probable decision using a robust aggregation operator. A common class of algorithms employed for this purpose is based on extensions of the Choquet integral (CI). In this study, we introduce and extensively analyze a novel aggregation operator concept founded on the generalization of the CI. This approach leverages quadrature formulae to calculate Choquet integral values, but with a unique modification involving a smoothing operation. This refinement results in more precise values, preserving the essential characteristics of the Choquet integral. These refined values can be effectively applied in the aggregation of classifiers and, more broadly, in information fusion processes. A series of numerical experiments demonstrates the efficiency of our approach. Furthermore, we thoroughly discuss and provide mathematical proofs for the properties of the newly constructed operators.