Applications Of Rough Sets In Attribute Reductions And Data Compressions

Rough set theory as an efective mathematical tool to deal with uncertain andimprecise problems has been applied to various areas such as data mining, artifcialintelligence and pattern recognition. Current research regarding rough sets main-ly focuses on two aspects: theory and its applications. Among them, attributereductions is the most important problem for rough set theory. For attribute re-ductions, on one hand, researchers have proposed efective attribute dependencydegree functions. But some functions are not ft for incomplete information sys-tems. On the other hand, on the basis of homomorphisms between informationsystems, researchers have presented an approach to attribute reductions by com-pressing information systems. But there is not much research on other types ofinformation systems. Furthermore, researchers paid a little attention to attributereductions and approximations of concepts with respect to dynamic informationsystems.In terms of computing the attribute dependency degree, Yamaguchi present-ed a new attribute dependency degree function for complete information systems.But there are some issues on applying it to incomplete information systems. Forcomputing the attribute dependency degree, we introduce three attribute depen-dency degree functions for incomplete information systems, and apply them to12data sets. Then we conduct the simplifcation for discernibility matrixes of incom-plete information systems with the proposed function. The experimental resultsshow that our proposed functions are more fexible to calculate the degree of eachconditional attribute related to the decision attribute for incomplete informationsystems.With respect to approximations of concepts, Wang Shiping et al. transformedcomputing approximations of concepts into the computing of characteristic matrix-es, but there are few studies on the approach to computing characteristic matrixes.To compute approximation of concepts, we propose two approaches to computingcharacteristic matrixes. Then, by using an incremental approach, we computecharacteristic matrixes of the dynamic covering without running the matrix acqui-sition algorithm repeatedly. We mainly address the characteristic matrix updatingfrom three aspects: the variations of blocks in the covering, the immigration andemigration of objects and the changes of attribute values. Several illustrative exam-ples are employed to show that the time complexity of constructing characteristic matrixes of the dynamic covering can be reduced signifcantly with the proposedapproach.For the compression of covering approximation spaces, we introduce the con-cepts of upper and lower homomorphisms as well as homomorphisms in order tostudy the relationship between covering approximation spaces. Then the notionsof covering approximation subspaces and product spaces are presented and theirfundamental properties are examined. Afterwards, we investigate the compres-sion of covering approximation spaces and covering information systems with theaim of reductions. Finally, we discuss the compression of dynamic covering ap-proximation spaces and dynamic covering information systems by utilizing thecompressions of the original spaces and systems, respectively. Several illustrativeexamples are employed to demonstrate that the homomorphisms provide an efec-tive approach to the compression of covering approximation spaces and coveringinformation systems.For the compression of set-valued information systems, we put forward threerelations for set-valued information systems and explore their basic properties indetail. Then the compression is investigated for attribute reductions of set-valuedinformation systems. Afterwards, we discuss the compression of dynamic set-valued information systems by utilizing the precious compression of the originalsystems. Several illustrative examples are employed to show that attribute re-ductions of set-valued information systems can be simplifed signifcantly by ourproposed approach.This dissertation has developed efective approaches to approximations of con-cepts and attribute reductions of information systems especially for dynamic in-formation systems. It enriches the rough set theory and attribute reductions ofinformation systems.