Research On Constructive Three-way Decisions Model

The three-way decisions model is one of the core ideas of rough set, which adds a third option to the common used binary-decisions model. The three-way decisions model regards boundary decision as a feasible decision.The Bayes Risk Decision Theory is introduced into the Decision Theoretic Rough Set, which makes this three-way decisions model fault-tolerant and provides more reliable theoretical basis and semantic interpretation in the uncertainty knowledge acquisition and data processing. That is to say, the model possesses fault tolerance and risk cost sensitivity when dealing with classification problem. The model can compute the thresholds (α,β) based on loss function which is given by experts, and divide the three regions based on the thresholds. In view of the threshold, Zhang proposed the Three-way Decisions based on Constructive Covering Algorithm. The advantage of the model is that it does not need any thresholds to divide three regions. The model gets three regions based on covers. And the model can do further process on the samples in boundary regions.However, compared with the Decision Theoretic Rough Set, the Three-way Decisions based on Constructive Covering Algorithm lacks of cost sensibility and fault-tolerant ability. At present, as the data mining and machine learning techniques are widely used in practical problems, more and more people find that the actual classification problems usually have cost sensitive characteristics. Therefore, this dissertation puts forward two kinds of improved model:1. Cost Sensitive Three-way Decisions Model Based on Constructive Covering Algorithm, which introduces cost sensitive into Three-way Decisions Model Based on Constructive Covering Algorithm. The purpose of introduction is reducing loss cost as far as possible.2. Robust Three-way Decisions Model Based on Constructive Covering Algorithm, which possesses better anti-noise ability and fault tolerance.In this dissertation, the main work includes:1. The dissertation introduces the development of theory of three-way decisions, and describes. We describe the research status of the theory, introduce cost sensibility and robustness into the three-way decisions model based on constructive covering algorithm, and propose Cost Sensitive Three-way Decisions Model Based on Constructive Covering Algorithm and Robust Three-way Decisions Model Based on Constructive Covering Algorithm. It provides a new idea to deal with the classification of sensitive data set and data set with noise by three-way decisions model.2. The Cost Sensitive Three-way Decisions Model Based on Constructive Covering Algorithm divides the data set according to the loss function to adjust the regions. We compute the number of each cover, and find that most samples are in fewer covers. In other words, most covers cover fewer samples. We cut the covers that contain few number of samples, and find that the impact on the sample classification accuracy is relatively small. The model adjusts the positive regions and negative regions according to cut covers of smaller radius. We introduce into cost sensibility and decrease the loss of classification by decreasing loss function of misclassification number. The model possesses the lowest total cost of classification in case to ensure accuracy of data classification.3. The Robust Three-way Decisions Model Based on Constructive Covering Algorithm enhances robustness by changing compute method of radius. The radius of cover in this model is changed by controlling number of negative samples in positive cover and number of positive samples in negative cover. The method enhances ability to resist noise. At the same time, we find that the area of cover extend with number of fault tolerant heterogeneous samples increasing. By adjusting the extend of the cover, we can change the area of positive region and negative region. Therefore, the model possesses robustness and cost sensibility.