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

The Choquet integral is an extension of Lebesgue integral and mathematical expectation in generalized measure theory. It's not easy to approximate the Choquet integral in the continuous case on a real line. The Choquet integral should be primarily estimated for non-additive measures. There are few studies on approximating the Choquet integral in the continuous case on real lines. No research has been done on the midpoint rule for the Choquet integral. The main objective of this paper is to propose some applications of the midpoint rule for approximating continuous Choquet integrals. By using the Choquet-midpoint rule, we can numerically solve Choquet integrals, specifically singular and unbounded integrals. Our proposed methodology is illustrated through several numerical examples.