The Extended Theory And Application Of Three-way Decision

The three-way decision theory is the promotion of the two-way decision theory.It divides the object into the accepted domain,the rejected domain,and the boundary domain to ensure the final decision result keeps the class to be judged,and avoid the risk of direct acceptance or rejection.Because the traditional three-way decision theory requires the decision cost table to solve the threshold which made the efficiency low,so a Bayesian factor is introduced to improve the classification efficiency.On the other hand,the traditional three-way decision theory cannot handle the situation of dividing objects into more categories,so this article made the following researches based on the three-way decision theory.Adding Bayesian factor into the traditional three-way decision theory improves the efficiency of classification.In this paper,we give the information table which including the set of all the research objects,the set of all the attributes of the object,the set of all the values of the attributes and the information function of all the research objects.Then determine the equivalent relationship R and according to the rule of ”if an object belongs to a positive domain,then the object's posterior probability must be greater than the prior probability ”to induce the three-way decision model based on Bayesian factor.After that,giving the threshold table,finally combine with the model and threshold table to achieve the division of objects.Then give an empirical analysis of the three-way decision model based on Bayesian factor,classifying the pinworm and concluding that the classification efficiency of the proposed model is higher than that of the traditional three-way decision model.Secondly,considering that the traditional three-way decision theory can only divide the objects into two categories,this paper considers extending the traditional three-way decision theory and proposing four-way decision theory.After the information table of the objects is given,then give the set descriptions of the objects which are divided into three categories and one boundary class,and then induce the evaluation function,along with the threshold to further describe the four categories.Then the thresholds can be gotten by the classification cost table and the loss function.The method of solving the evaluation function of each type of object is also given respectively.Finally,all the objects are classified according to the evaluation function and the thresholds.Then we give an empirical analysis of the four-way decision theory–classifying iris flowers.The result shows that the false classify rate is 1.3% compared with the K-means clustering result which of the false classify rate is 6%,this verified the conclusion that the four-way decision model is better.Finally,the four-way decision theory are further extended to the N-way decision theory,which can divide the research object into any number of categories.Firstly,a set description of the research objects is giving,and then induce the evaluation function,along with the threshold to further describe the N classes.Then use the classification cost table and the loss function to get the thresholds.The method of solving the evaluation function of each type of object is also given respectively.Finally,all the objects are classified according to the evaluation function and the thresholds.