Capacity-Based Definite Rough Integral and Its Application.

This paper introduces an extension of the original capacity-based rough integral defined over a specific interval. The approach hearkens back to the pioneering work on capacities and the generalization of the Lebesgue integral by Gustav Choquet during the 1950s. Variations in the definition of the capacity function has led to various forms of the discrete Choquet integral. In particular, it is the rough capacity function (also called a rough membership function) introduced by Zdzislaw Pawlak and Andrzej Skowron during the 1990s that led to the introduction of a capacity-based rough integral. By extension of the original work on the rough integral introduced in 2000, a discrete form of a capacity-based definite rough integral is introduced in this paper. This new form of the rough integral provides a means of measuring the relevance of functions representing features useful in the classification of sets of sample objects.