Attribute Reducts and Decision Rules in Real Valued Information Systems with Fuzzy Decision

Abstract

For real valued information systems with fuzzy decision, based on the concept of supporting set of decision interval, two types of relative reducts are defined, that is, the relative reduct of the maximal tolerance class and the relative reduct of the fuzzy relation. For the first type of relative reduct, the computing method based on the discernibility function is given. For the second type of relative reduct, the computing method based on the discernibility function and a heuristic algorithm are given, respectively. Moreover, the relationship between the two types of reducts is investigated. Finally, based on the maximal tolerance class related to the condition attributes and the lower approximation of the supporting set of decision interval, the decision rules are obtained, and the optimal decision rules are calculated using the first type of relative reduct.