A Study On Attribute Reduction Based On Neighborhood And Fuzzy Rough Sets

Attribute reduction can be fully expanded and used in rough set theory. This thesis mainly explores attribute reduction from two aspects which are neighborhood and fuzzy rough set theory. At the same time, the correlated model is established. They are Boolean matrix attribute reduction model based on neighborhood rough set and distance measure attribute reduction model based on fuzzy rough set. Then, algorithms are designed respectively in the basis of these two models. Meanwhile, the thesis analyzes experiment using the UCI data sets, which confirms the effective of the algorithm.1. Attribute reduction model of Boolean matrix based on neighborhood rough set.This thesis defines the Boolean matrix attribute reduction model based on the concept of neighborhood. Firstly, the thesis constructs the conditional attribute Boolean matrix and decision attribute Boolean matrix, introduces attribute importance evaluation index based on Boolean matrix by analyzing their relationships and operations. Secondly, it is proved that the equivalence relationship between the index and classic dependent function index. Finally, this thesis designs the feature selection algorithm based on Boolean matrix and analyzes the algorithm’s reduction performance.2. Attribute reduction model of distance measure based on fuzzy rough set.This thesis firstly introduces fuzzy similarity relation based on distance, discusses their simple properties and redefines upper and lower approximation of fuzzy decision. Then, the concept of positive region is defined. According to the concept of positive region, the thesis constructs dependence degree function based on distance measure, which is importance evaluation index. The algorithm is illustrated effectively by the data analysis.