Research Of Logic Foundation And Modelson Three-way Decision

The rough sets theory has achieved many important outcomes in theoretical and applied research as a method dealing with uncertain problems.The universe would be divided into positive region,negative region and boundary region by rough sets theory,and the process of dividing was data-based and objective,without pretreatment and prior information.The three-way decision theory was came up based on decision-theoretic rough sets upon Bayes decision-making by Yao from University of Regina in Canada at 2010.Delayed decision was add to the three-way decision theory with development of the two way decision including acceptance and rejection.The event objects of positive region would be classified as acceptance;the event objects of negative region would be classified as rejection;the event objects of boundary region would be classified as deferment.Delaying decisions would avoid the loss of forcing to choose acceptance or rejection.The study of three-way decision theory has has gradually in a hot research because the three-way decision could reflect the world more naturally.At present,there are four main research directions: theoretical models,methods of study,decision rules and application.These studies were limited to decision-theoretic rough sets which causes the imperfection on basic research of three-way decision theory.According to the above analyses,the truth table and logical reasoning process of three-way decision was structured based on logical system K3 and triple-tree theory;the static model and the dynamic models of three-way decision theory was structured based on intuitionistic fuzzy sets theory;the methodology of attribute weights acquisition of three-way decision theory was structured based on condition attribute theory.Finally,these studies of the proposed methods and models were provided to demonstrate the effectiveness and feasibility.The innovative points of the research are as follows:(1)Combing 3-valued logic systems K3 with the three-way decision theory,which was based on decision-theoretic tough sets and three-valued logic,truth tables of event objects in the state of competition,cooperation and general were came up with constructing the logical model of three-way decision.Meanwhile,the process of logical reasoning was described through traversal with three-way decision threes intuitively.(2)The 2-state,3-state model of three-way decision theory based on intuitionistic fuzzy sets were came up and expand to the general static model.The model redesigned the threshold value with hesitancy degree and assessed the event objects by the membership function.At last,the experimental results show that the model was effective.(3)On the basis of general model of three-way decisions theory based on intuitionistic fuzzy set theory,the dynamic model was structured with possibility degree matrix in fuzzy comprehensive evaluation.The model brought three-way decision into two way decision and realized dynamic classification of event objects.Then the experimental results show that the model was feasible.(4)Two definitions of the attribute confirming and attribute reduction were redefined respectively,anew weight on attribute method was presented and also compared with the conclusions of the example got by other methods,then the efficiency of the presented method was demonstrated.Based on the research above all,the theory has been enriched,and the application range of the three-way decision has been expanded.