Study On Variable Precision Rough Set Model And Its Application

Rough set theory is a new mathematical tool for dealing with fuzzy and uncertain knowledge. It contacts classify and knowledge according to indiscernible relation of known data and expresses some concepts approximately by a pair of approximation operators. it is a data driven approch and do not need any prior knowledge and additional information about data and corresponding problems, so it is fit for applying to fields of knowledge discovery and data mining. Ziarko has proposed variable precision rough set model(VPRSM) because of shortcomings of Pawlak's rough set model, which is inheritance and development of Pawlak's rough set model, but it is still confined by equivalence relation. In this paper, to enlarge application range of VPRSM, firstly, theory and approach of boundary preserved attributes reduction have been proposed, secondly, VPRSM has been popularized from universe and the relation on it, that is to say universe is popularized from crisp sets to fuzzy set on universe and equivalence relation on universe is popularized to general binary relation, covering relation and fuzzy relation. The generalized variable precision rough set model, variable precision covering rough set model, variable precision rough fuzzy set model, variable precision fuzzy rough set model are obtained. Concrete achievements are as follows:1. Boundary preserved attributes reduction theory and approaches of information system have been proposed based on VPRSM. In Ziarko's VPRSM, the properties of boundary preserved reduction are studied and judge theorem of reduction is given. Using discernibility function and matrix, the approaches of reduction and algorithms of reduction are given. Finally, the effectivity of this algorithm is illustrated through examples. Proposed reduction approaches in this paper enrich attributes reduction theory of VPRSM and point out a effective approach for database knowledge discovery under equivalence relation.2. Generalized variable precision rough set model has been established. In Ziarko's VPRSM, equivalence relation on universe is popularized to general binary relation, we establish two kind of generalized variable precision rough set models based on objects and successor neighbor operator. The structure and properties of approximation operators in these two kinds, the relationship among approximation operators and the relationship between these two models and Ziarko's VPRSM are discussed in detail. Finally, uncertain measurement approaches, such asβapproximation quality andβrough measure of concepts in these models, arestudied.3. Variable precision covering rough set model has been established. In Ziarko's VPRSM, when equivalence relation on universe is popularized to covering relation, having the aid of successor neighbor operator produced by covering, we establish two kind of variable precision covering rough set models. The structure and properties of approximation operators in these two kinds are studied. The relationship among approximation operators and the relationship between these two models and other rough set models, and the relationship between these two variable precision covering rough set models and Ziarko's VPRSM are discussed in detail. Finally, the reduction of covering in variable precision covering rough set model is also discussed.4. Variable precision rough fuzzy set model has been established. In Ziarko's VPRSM, when equivalence relation on universe is popularized to fuzzy relation, variable precision rough fuzzy set model and average variable precision rough fuzzy set model are established. The structure and properties of approximation operators in corresponding models and the relationship between these two models and other rough set models are studied.5. The algorithms of knowledge discovery and rules mining have been established based on variable precision rough set model. A complete calculation process is proposed by using uncertain measurement, the effect analysis and algorithms of threshold values on the variable precision rough rules set. This approach has a certain noise tolerance ability and can obtain succincter rules set under more precision and better overlay. The effectivity of this algorithm is illustrated by examples.The theory of all kinds of variable precision rough set model has been discussed based on static complete data in one universe and the application approaches of these models has given, which have important theoretical values and practical meaning for database knowledge discovery. These models solve knowledge discovery problems between different kinds of data and different data relation, which are supplements and developments of rough set theory and enrich knowledge discovery theory and approach. These models have important theoretical meaning and will have potential applied values.