The Study Of Generalized Rough Set Models Based On Different Knowledge Granules

Rough set theory has been conceived as an effective mathematical tool for dealing with uncertain information. It provides the theoretical foundation for processing the incinsistent and incomplete problems in information systems. Rough set model is based on the knowledge granules determined by the binary relation. The size of knowledge granule directly impacts on the data mining capacity of the rough set model. The oversize knowledge granule will weaken the character of the rough set model, while the small knowledge granule will reduce its generalization abilities. So it is necessary to select suitable knowledge granule for constructing the rough set model. With a view to basic knowledge granule, this paper focuses on the properties and characters of generalized rough set models based on different knowledge granules. This study can deepen our knowledge of the generalized rough set models. In the paper, the connections of the tolerance rough set models based on the tolerance classes and maximal tolerance classes are discussed. The dominance-based rough set approache based on the interval knowledge granules and the generalized rough set models based on predecessor sets and successor sets are also mentioned. This paper is organized as follows.In Chapter 1, the state of the art of tolerance rough set models, dominance-based rough set models and some generalized rough set models are introduced. The framework and innovations of this paper are also given in this chapter.In Chapter 2, some basic concepts and mathematical properties of Pawlak rough set model, tolerance rough set models, dominance-based rough set models, generalized rough set models are reviewed, such as equivalence class, tolerance class, maximal tolerance class, dominate set and dominated set, lower and upper approximations, dual property.In Chapter 3, the properties and relationships of some existed lower and upper approximations based on the tolerance classes and maximal tolerance classes are discussed. And some new kinds of lower and upper approximations are defined by used of the maximal tolerance classes, and their mathematical properties are also discussed. Moreover, the relationships among the approximations in original tolerance rough set model, Leung’s approximation, Guan’s approximations and the new approximations are researched. At last, some suggestions for choosing the suitable lower and upper approximations are given for the purpose of improving approximation accuracy.In Chapter 4, some basic concepts of dominance-based rough set approach based on intervals in complete ordered decision information system(ODIS) are introduced. This new dominance-based rough set approach can be extended to incomplete ordered decision information system(IODIS), and derives the “at least and at most” decision rules. To optimize the decision rules, the relative reduct of an interval is defined, and the discernibility function is constructed to compute the relative reducts. By the relative reducts, corresponding optimal “at least and at most” decision rules are obtained.In Chapter 5, the lower and upper approximations in generalized rough set models are studied. The positive object, ambiguous object and negative object are redefined in term of the predecessor sets and successor sets. For some kinds of binary relations, the detailed discussion for the relationships between positive object, ambiguous object, negative object and lower(upper) approximations are given, respectively. And some suggestions for choosing a pair of suitable lower and upper approximations of a given subset are presented in generalized rough set models.In Chapter 6, we summarize the whole thesis and look forward to the future work.