Function Approximation and Quality Measures in Rough–Granular Systems

Abstract

We discuss the problem of measuring the quality of decision support (classification) system that involves granularity based on rough set concepts. We put forward the proposal for such quality measure in the case when the underlying granular system is based on rough sets and makes use of approximation spaces. We introduce the notion of approximation, loss function, and quality measures that are inspired by empirical risk assessment for classifiers in the field of statistical learning. We further discuss the possibilities of improving the quality measure by extrapolating the loss function using function approximation methods originating in extensions of the concept of approximation space.