Knowledge Reductions In Nondiscrete Information System Based On Rough Set Theory

Classical rough set approaches focus on complete and discrete information system, in which attribute value is just a symbol that expresses a feature of one object. Extensive researches on them have been done and some results have been presented. However, there are also many incomplete or nondiscrete information systems, which is difficult to deal with or get forecast effect by classical rough set models.In this paper, we are concerned with applications of extension rough set models in information systems, especially attribute reductions and optimal decision rules acquisitions in nondiscrete information systems. The paper is structured as follows:In chapter 3, knowledge reductions in two types of incomplete information system are studied.In section 1, we discuss a new approach to knowledge acquisition in information system; in which lost and"do not care"unknown attribute values are coexisting. In such incomplete information system, we classify the universe of discourse by the maximal tolerance classes, and the relative reductionions of maximal tolerance classes are introduced firstly, decision rules based on the proposed attribute description are defined. Then the judgment theorems are given, and discernibility functions with respect to them are constructed and used to compute the relative reductionions of maximal tolerance classes by utilizing Boolean reasoning techniques. From the relative reductionions of maximal tolerance classes, we can derive optimal decision rules. Finally, computing methods of relative reductionion of the system and their computing methods are given.In section 2, we discuss the attribute reduction in inconsistent set-valued decision information systems. Firstly, the universe of discourse is classified by tolerance relation, which is defined by similarity degree of attribute values. Then concepts of lower and upper approximation reduction, lower and upper distribution reduction are introduced, the relationship among them are discussed. Finally, the judgment theorems and discernibility functions with respect to lower and upper distribution reduction are obtained, from which computing methods of attribute reduction in inconsistent set-valued decision information systems can be derived. In chapter 4, knowledge reductions in three types of fuzzy-valued information system are studied.In section 1, Definitions of three new types of attributes reductions of objects in fuzzy objective information systems are introduced respectively. The judgment theorems and discernibility functions with respect to these types of reductions are proposed, from which computing methods of attributes reduction of objects can be derived. Based on these reductions, three new types of optimal decision rules are obtained, and the degree of certainty of them are discussed. At last, three kinds of attributes reduction of the systems and their computing methods are given.In section 2, a new approach to knowledge acquisition in incomplete information system with fuzzy decisions is proposed. In such incomplete information system, the universe of discourse is classified by the maximal tolerance classes, and fuzzy approximations are defined based on them. Three types of relative reductions of maximal tolerance classes are then proposed, and three types of fuzzy decision rules based on the proposed attribute description are defined. The judgment theorems and approximation discernibility functions with respect to them are present to compute the relative reduction by using Boolean reasoning techniques, from which we can derive optimal fuzzy decision rules from the systems. At last, three types of relative reductions of the system and their computing methods are given.In section 3, for fuzzy information system with fuzzy condition attributes and fuzzy decision attributes fuzzy indiscernibility relation is induced by considering the similarity between the two objects, by which indiscernibility relation in classical rough set model can be replaced firstly. Secondly, concepts of consistence degree of objects are proposed, further attribute simplifications of objecets are discussed by introducing a threshold, simplified decision rules are induced. Finally, the simplifications of the system are discussed.In chapter 5, for interval-valued decision information system, we classify the universe of discourse by the maximal tolerance classes, and theβ- relative reductions of maximal tolerance classes are introduced firstly,β- decision rules based on the proposed attribute description are defined. From theβ- relative reductionions of maximal tolerance classes, we can deriveβ- optimal decision rules. Finally, computing methods ofβ- relative reductions of the system and their computing methods are given.