Generalized decomposition integral of real functions with respect to fuzzy measures

TL;DR

This paper introduces a generalized integral for non-negative real functions with respect to non-additive measures, extending classical properties of the Riemann-Lebesgue integral.

Contribution

It defines a new type of decomposition integral with respect to fuzzy measures, broadening the scope of integration theory.

Findings

Established classical properties of the new integral

Extended integral concepts to non-additive set functions

Provided a theoretical framework for generalized integration

Abstract

In this paper we define a type of generalized Riemann-Lebesgue (decomposition) integral for non-negative real functions with respect to two non-additive set functions. For this integral we present some classical properties.