Research Of Variable Precision Fuzzy Rough Sets Theory And Its Application

As a new theory of data analysis the rough sets are an important mathematical method to deal with uncertainty problems. It is widely applied in various fields such as data mining, machine learning, artificial intelligence and pattern recognition. But there are some shortcomings about classical rough sets theory. Pawlak's rough sets model and the variable precision rough sets model are built on equivalence relations. But in practical applications, many objects we handle are fuzzy, and there are no crisp relations between one object and another but only fuzzy relations.Attributes reduction is a NP problem, and the conventional optimization can't be used successfully. In this thesis the ACO algorithm is used to solve this problem. On the basis of the feature of attributes reduction,the state transition probability formula and the pheromone updata formula are modified to make it more adaptive to attributes reduction.This thesis proposes the variable precision fuzzy rough sets model on the basis of fuzzy similarity relations, which assimilates the idea of Ziarko's variable precision rough sets. Then the rough approximations of fuzzy sets are studied, and particularly the properties of variable precision fuzzy rough sets are investigated. Pawlak's rough sets and the Ziarko's variable precision rough sets are two instances of the model proposed.In clustering analysis, different attributes have different importance in clustering, and even some attributes disturb the clustering results. In this thesis, the variable precision fuzzy rough sets model is applied in calculating the weights of attributes. The weights of attributes are analyzed by variable precision fuzzy rough sets model and the notion importance of attributes. Then the result is applied to FCM algorithm. Experimental results show that the attributes with different weights which are analyzed by variable precision fuzzy rough sets greatly improve the quality of clustering.