Research On Approximation Sets Of Rough Sets And It's Application

Rough set theory proposed by professor Pawlak in 1982 is an important mean to solve the uncertain problems, and it describles the uncertainty of a target set X?or concept? with two crisp boundaries that are upper-approximation set and lower-approximation set of X. However, there are few theories and methods for dealing with how to use the existing knowledge base to approximately describe an uncertain target set X. In this thesis, on the basis of basic theory and the latest research results about the existing approximation sets of rough sets, the optimal approximation sets of rough sets theory and rough sets application will to be discussed. By studing and exploring the above aspects, the related research results are presented.?1? In this thesis, firstly, the concept of the similarity between two sets and the construction method of fuzzy approximation set of rough sets were reviewed, and the properties of operation are proposed and proved. Secondly, the existing interval of ? in which R_??X? is more similar to the target concept X than both the upper-approximation set R?X? and lower-approximation set R?X? are presented. Finally, the conditions of R_0.5?X? as an optimal approximation set of the target concepts X are found. On the basis of the above study, the optimal approximation sets of rough sets theory are proposed. First of all, the optimal approximation set R_Best?X? will to be defined and the algorithm for constructing an optimal approximation set will to be given. What's more, in the different knowledge granularity spaces, the change rules of the similarity between a target X and its R_Best?X? with the changing knowledge granularity will to are discussed in details. From the viewpoint of computation, the optimal approximation set R_Best?X? of X is discovered and its constructing method is established. These research results will promote the development of uncertain information process from the new perspective, i.e., a kind of new idea for approximately describing a rough set?or uncertain concept? probably is applied to deal with more vague problems.?2? In the previous study, approximation sets of rough sets model was used for the attribute reduction. However, it also has some problems as follow. Firstly, it puts forward the algorithm of Attribute Reduction based on similarity, but does not give some theories to support it. Secondly, similarity is not sensitive to the changes of knowledge granularity so that it may miss some useful attributes in process of attribute reduction. In this thesis, firstlythe change rule of similarity in a hierarchical approximation space is presented and the rationality of using similarity to attribute reduction is shown. Secondly a concept namely, fuzzy degree of approximation set to remedy the shortage of similarity is defined. Finally, the change rule of the fuzziness of approximation set in the hierarchical approximation space is analyzed, and the uncertainty also can be applied in attribute reduction. From a new perspective, the diversity measurement between a target concept of X and its approximation set is presented, and these researches probably promote the development of rough set theory.