Three-way Decisions Model Based On Constructive Covering Algorithm

The concept of three-way decisions was recently proposed and used to interpret three regions of rough set. More specially, the positive, boundary and negative regions are viewed, as the regions of acceptance, rejection, and noncommitment in a ternary classification respectively. It is an extension of the commonly used binary-decision theory with an added third option.The study of three-way decisions is mainly based on Decision Theoretic Rough Set, which is proposed by Yao in1990. The essential ideas of three-way decisions are commonly used in everyday life and widely applied in many fields and disciplines. However, there are still some problems need to be solved in the three-way decisions of rough set model:1. In this model, a pair of thresholds α,β form the three regions, but the thresholds are computed by loss functions and the loss functions are given by experts, which are unreliable;2. The model only classifies samples into three regions, but do not do any further processing with the samples in boundary regions.The main work of this dissertation is to introduce Constructive Covering Algorithm (CCA) into three-way decisions, and proposes a three-way decisions model based on CCA. The model can form three regions automatically according to the distribution characteristics of samples. Compared with the three-way decisions model based on decision-theoretic rough set, the three-way decisions model based on CCA can form three regions automatically and do not need any parameters. The new model solves the problem that parameters are given by experts. On the other hand, two methods to deal with samples in boundary region are proposed based on the new model. They are deal with all samples in boundary region and deal with part of samples in boundary region.The work includes:1. The development of theory of three-way decisions is introduced. We describe the existing three-way decisions models in detail, introduce CCA into three-way decision and propose a new three-way decisions model based on CCA. The new model can form three regions automatically according to the distribution characteristics of samples, which do not need any given parameters. We describe the method to form three regions, and how to classify samples based on the three regions. Four public datasets are used in the experiments to evaluate the performance of the new model. The experiment results show that the classification accuracy of the new model has a significant improve on some part of the data sets. And meanwhile, the new model also provides a new solution of forming three regions.2. According to the new three-way decision model based on CCA, we provide two methods to deal with samples in boundary region. The first one is dealing with all samples in boundary region, which has three principles:the nearest to the center principle, the nearest to the boundary principle, gravity principle. The second one is dealing with part of samples in boundary region. That is to say, we only classify the samples in boundary region which satisfy certain conditions, and do not deal with the rest samples in boundary region. The reason is that we process the samples which are easy to distinguish relatively, and do not process the samples which are difficult to distinguish. Five public datasets are used in the experiments to evaluate the performance of those two methods. The experimental results show that the method dealing with part of samples in boundary region is better on classification accuracy.