On an extension of the Choquet integral for multi-valued data

Abstract

In this paper, we propose a new generalization of the classical Choquet integral that admits an input composed of n functions and returns a single scalar output. We study its fundamental properties and show that it is an aggregation operator. Furthermore, we use the proposed integral to extend the notions of covariance and variance to the case of uncertainty based on monotone measures, and indicate the area of potential application of the introduced extensions. We also demonstrate how to define the average value of a finite sequence of vectors using the new integral, provide an adaptation of Sugeno's method for calculating the integral from monotone functions and present some integral type inequalities.