Approximating Choquet integral in generalized measure theory: Choquet-midpoint rule

Abstract

In generalized measure theory, Choquet integral is a generalization of Lebesgue integral and mathematical expectation. Approximating Choquet integral in the continuous case on real line is not very easy. So, we need mainly to estimate Choquet integral with respect to non-additive measures. There are few studies on the approximating Choquet integral in the continuous case on real line. In approximation theory, there are many interesting properties of midpoint rule. As a subject for research, there are no results on the midpoint rule for Choquet integral. The main objective of this paper is to propose some applications of midpoint rule for approximating continuous Choquet integral. The choquet-midpoint rule helps us to numerically solve Choquet integrals, in particular, the singular and unbounded integrals. Several numerical examples are considered to illustrate the application of our proposed methodology.