Research On The Theory And Application Of Three-Way Dicisions

Three-way decisions theory is an extension of the traditional two decisions theory. In the traditional two decisions, only acceptance and rejection two ways are considered. But in real life, the decision problems people faced with often have the characters of uncertainty, incompleteness and inaccuracy, and all these lead that people can’t make a decision with acceptance or rejection immediately. Three-way decisions theory added a disclaimer choice on the basis of the traditional two decisions theory, namely, people will use the disclaimer option when they can’t make a decision immediately because of the lack of information, and it also can be regarded as deferment. The three-way decisions theory is put forward on the basis of the research on rough sets and decision-theoretic rough sets, and it provides a reasonable semantic interpretation for the three domains in rough set model: the rules obtained from the positive region are used to accept something; the rules obtained from the negative region are used to reject something; the rules obtained from the boundary region means that more detailed observations are needed, in other word, deferment. The three-way decisions describe the human thinking mode in dealing with practical decision-making problems very well. And now, it has been widely used in many subjects and fields, including medical diagnosis, social judgment theory, hypothesis testing in statistics, the paper review and management etc.This paper makes research on the three-way decisions from two aspects of theory and application respectively, the main contents are listed as follows:(1) Aiming at the problem that there are some limitations when use the classical Pawlak rough sets to solve the questions described in Vague sets, in the perspective of three-way decisions, the new explanations and definitions of the membership degree of Vague sets were given through making use of the conditional probability, a pair of thresholds(?, ?) and the risk of loss function ?. Comparing with that using the upper and lower approximation sets derived from algebraic inclusion relation in rough sets to describe the membership degree, the idea above not only can enhance the application ability of Vague set model, but also can make it more interpretable when use the Vague set model to solve practical decision-making problems. In addition, by analyzing the relationship between the two kinds of collections, the three-way decisions partition based on Vague sets was put forward and its three domains were defined using the membership functions tV(x), 1- fV(x) combined with the threshold value of(?, ?), then, the corresponding three-way decision rules were obtained; at the same time, the definition of the membership function of Vague sets was given, and some related properties of them were researched. The study above not only perfects the three-way decisions and Vauge sets theories, but also has a contain theoretical and application values for the research on the combination of these two theories in the theory and application aspects.(2) In order to overcome those defects that the fuzzy membership degree acting as the state function dose not satisfy the normalization and additivity, and solve the problem that the max-min operation of fuzzy sets will lose a lot of useful information in the evaluation of the venture investment, the Bayesian theory and the three-way decisions were introduced into the fuzzy comprehensive evaluation model in this paper. At First, a new risk factor was defined with the risk function instead of the fuzzy membership degree and a new risk evaluation matrix was constructed with the new risk factor, then the risk investment evaluation model based on the three-way decisions was proposed; In addtion, by the principle of risk minimization decision-making mode, take the decision in accordance with the minimum risk loss value as the final evaluation result. Through comparing with the fuzzy comprehensive evaluation model, the risk investment evaluation model based on three-way decisions not only can solve the defects existing in the fuzzy comprehensive evaluation model, but also can make the evaluation results more reasonable, accurate and interpretability.