Rough Measures and Integrals: A Brief Introduction

Authors:
Zdzislaw Pawlak;James F. Peters;Andrzej Skowron;Zbigniew Suraj;S. Ramanna;Maciej Borkowski
Affiliations:
-;-;-;-;-;-
Venue:
Proceedings of the Joint JSAI 2001 Workshop on New Frontiers in Artificial Intelligence
Year:
2001

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Abstract

This paper introduces a measure defined in the context of rough sets. Rough set theory provides a variety of set functions that can be studied relative to various measure spaces. In particular, the rough membership function is considered. The particular rough membership function given in this paper is a non-negative set function that is additive. It is an example of a rough measure. The idea of a rough integral is revisited in the context of the discrete Choquet integral that is defined relative to a rough measure. This rough integral computes a form of ordered, weighted "average" of the values of a measurable function. Rough integrals are useful in culling from a collection of active sensors those sensors with the greatest relevance in a problem-solving effort such as classification of a "perceived" phenomenon in the environment of an agent.