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

Year 2024, Early Access, 1 - 9

Mahmoud Behroozifar

https://doi.org/10.15672/hujms.1463439

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.

Keywords

Choquet integral, Derivative with respect to non-additive measure, Numerical Choquet integration

Supporting Institution

No support

Project Number

No Project

References

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