Research Of Attribute Reduct And Extended Model In Ordered Information Systems

The dominance-based rough set models are established on the classification of universedetermined by dominance relation and has been proved to be an excellent mathematical toolto deal with uncertain, imprecise, and incomplete information systems. Knowledge reduct isone of most important fields in dominance-based rough set models. In ordered informationsystems, the attribute value can reflect preference relation, but not in Pawlak rough set models.To overcome this drawback, Greco, Matarazzo and Slowinski proposed the dominance-basedrough set approach by taking the ordering properties of attributes into account.Knowledge reduction is used to find potential, valuable, simple information from chaotic,strong interference and large data. In this paper, for several different ordered decisioninformation systems, we discussed the attribute reduction based on the dominance-basedrough set approach and its extended models. This paper is organized as follows:In Chapter1, the background and status of dominance-based rough set models areintroduced. The framework and innovation are given in this chapter.In Chapter2, some notations and basic concepts for classical rough set model and thedominance-based rough set approach such as incomplete, inconsistency, lower(upper)approximation, consistent objects and knowledge reduction are introduced.In Chapter3, Some concepts and properties in Pawlak rough set modle are comparedwith those in dominance-based rough set model, then the relationships among them are asfollows: the set of consistent objects in the PRSM is the union of lower approximations of allthe decision classes, and the set of consistent objects in the DRSA is the union of lowerapproximations of all decision classes rather than the union of lower approximations of allupward(downward) unions of decision classes. In the PRSM, the set of consistent objects andthe union of boundaries of all the decision class are complementary with each other. In theDRSA, the set of consistent objects is complementary with the union of boundaries of all theupward (downward) unions of decision classes, as well as with the union of boundaries of allthe decision classes. Accordingly, in the PRSM, the reduct preserving the set of consistentobjects equals the reduct preserving the quality of approximation, as well as the reductpreserving the lower approximation of every decision class. The reduct can be used to simplify all the certain decision rules. In the DRSA, the reduct preserving the set of consistentobjects is equivalent to the reduct preserving the quality of approximation, as well as thereduct preserving the lower approximation of every single decision class. However, it is notequal to the reduct preserving the lower approximation of every upward union of decisionclasses. The former reduct simplify all the certain bidirectional decision rules, and the lattercan be used to simplify all the certain “at least” and “at most” decision rules.In Chapter4, several reducts and their discernibility matrixes are discussed in orderedinformation systems. Firstly, we prove that the reducts preserving the lower(upper)approximations is equivalent to the compatible(possible) distribution consistent reducts inODIS and give a more simple approach for acquiring reducts. Then the consistent orderedpair reduct is proposed and it is an extension of dominance ordered pair reduct from orderedinformation systems to ordered decision information systems. Consistent ordered pair reductis computed by discernibility matrix and Boolean reasoning technique. At last, the reductpreserving consistent objects and consistent ordered pair reduct are two kinds of differentreducts by comparison of semantic interpretation, discernibility function and calculationmethod.In Chapter5, we discuss the properties of variable consistency dominance-based roughset approach, prove that the properties of original dominance-based rough set approach can begeneralized to the variable consistency dominance-based rough set approach. Therelationships between l-lower(upper) approximations and l-boundaries of unions of decisionclasses are discussed. Furthermore, we define the concept of l-lower(upper) approximationsand l-boundary of decision class, and research their relationships. By studying the propertiesof l-consistent object, we prove that the set of l-consistent object is the complementary set ofl-boundary, and the l-approximation quality is the ratio of l-consistent objects to all theobjects in the universe of discourse.In Chapter6, we conclude our work and look forward to the future work.