Efficiency of decision rule sets in fuzzy rough set theory

Abstract

Datasets have been interpreted in (fuzzy) rough set theory as decision tables to obtain useful information to be used, for example, in decision making. These tables have been modeled through a collection of decision rules, which was called decision algorithm by Pawlak. These algorithms are analyzed by the notion of efficiency, which evaluates their quality of classification. This paper presents two different approaches for defining the notion of efficiency in the fuzzy framework. The first approach is a direct generalization to the classical case, while the second one is focused on obtaining a bounded efficiency preserving the philosophy of the classical framework. Both approaches are illustrated by means of different properties and examples.