Attribute reduction and optimal decision rules acquisition in interval-valued information system

A new approach to knowledge acquisition in interval-valued decision information system is proposed. In an interval-valued information system, by using the similarity degree of two different objects, a fuzzy similarity matrix, which generates a tolerance relation with a given level, is constructed. The universe of discourse is classified by the maximal tolerance classes based on the tolerance relation, and attribute descriptions of maximal tolerance classes are proposed. By using attribute descriptions, decision rules are induced. In order to compute optimal decision rules, the relative reducts of maximal tolerance classes are proposed, the judgment theorems are given, and discernibility functions are constructed and used to compute the relative reducts by utilizing Boolean reasoning techniques. Finally, the concept of relative reduct of the system and its computing methods are discussed.