Knowledge Reduction In Ordered Information System Based On Dominance Relation Rough Set Theory

Classical rough set theory is based on the classification of universe determined by equivalent relation and successfully used in knowledge reduction of complete symbolic information systems. However, in ordered information systems, attribute values of the objects represent the dominance relation between the objects. Therefore, classical rough set theory, which is established based on the indiscernibility, is inapplicable in dealing with knowledge reduction problem of the ordered information systems. So Greco et al. proposed the dominance-based rough set approach to draw decision rules and compute reducts of the ordered information systems.In this paper, dominance-based rough set approach and its extended models are used to discuss attribute reduction and decision rule acquisition in ordered information systems. The paper is organized as follows:In Chapter 2, primary knowledge of ordered information systems and dominance-based rough set approach such as dominance relation, upper (lower) appproximation, ordered decision rules and knowledge reduction are introduced. In Chapter 3, the consistent reducts of ordered decision information systems are studied. Firstly, the definition of consistent reduct is proposed. Then, it is proved that the consistent reduct is actually a L - reduct as well as a Q - reduct. Finally, the discernibility function of the consistent reduct is constructed, and used to compute the consistent reduct by using Boolean reasoning techniques. By discussing the consistent reduct, we get a new computing method which employs discernibility function for Q - reduct.In Chapter 4, lower approximation reducts in inconsistent ordered decision information systems based on dominance relation are studied. We improve the computing method of lower approximation reducts proposed by other authors and construct a new discernibility function to compute the lower approximation reducts.In Chapter 5, attribute reduction and optimal decision rules acquisition problems in fuzzy objective ordered information systems are studied. Firstly, fuzzy lower approximation and fuzzy upper approximation are defined, three new types of decision rules generated by an object are proposed, and the degrees of certainty of the decision rules are given. Then, reduct of the object is defined, the judgment theorems are given, and discernibility function with respect to three types of reducts are constructed, by which reducts of the object can be derived. Based on these reducts, three new types of optimal ordered decision can be induced. At last, three kinds of reducts of the systems and their computing methods are given.In Chapter 6, conclusions of the work in this paper are given, and the future work is pointed out.