Function Approximation by Fuzzy Rough Sets

Abstract

This chapter provides an overview on the application of fuzzy rough sets to function approximation based on decision tables. A general approach for reasoning of decision attribute values from condition attribute values based on a given decision table is presented. A specific method in one-dimensional case is discussed and some properties of the method are shown in the chapter. Some modifications are applied for getting a better approximation and a smaller body of rules. By the methodologies based on rough sets, it is useful to find the reduced information tables without losing the accuracy of the object classification, and the minimum descriptive decision rules. These methodologies are effective when attribute values are discrete. To treat continuous attribute values, some discretization is necessary. Therefore, these methodologies are not good for the extraction of continuous functions implicit in given information tables. The application of fuzzy rough sets to approximation of a continuous function implicit in decision table has recently been proposed and it is still at a very beginning stage. This fact shows a possibility of treatment of continuous attributes in decision tables by means of fuzzy rough sets.