Three-Way Decisions Based On Intuitionistic Fuzzy Numbers In Incomplete Information Systems

Because of the three-way decision theory increases the delayed decision region,the losses caused by the wrong decisions are decreased.Therefore,in incomplete information systems and intuitionistic fuzzy information systems,combining the existing results of rough set theory,intuitionistic fuzzy set theory,and bayesian decision theory,intuitionistic fuzzy numbers are introduced into three-way decision models for decision analyses.Using more and more information,the objects in the delayed decision region are divided into the other regions.Thus,the objects in the delayed decision region can be made more proper decisions.Then the sequential three-way decision can be discussed.The contents of this paper can be described follows:Firstly,in incomplete information systems,the similarity degree and dissimilarity degree between two objects are defined.The similarity degree and the dissimilarity degree can be regarded as the membership degree and non-membership degree of an intuitionistic fuzzy relationship,respectively.Subsequently,we can use the novel defined intuitionistic fuzzy similarity relationship to get the level relationship of an intuitionistic fuzzy similarity relationship.Then,using a level relationship of an intuitionistic fuzzy similarity relation instead of an equivalence relation,a three-way decision model based on intuitionistic fuzzy numbers in incomplete information systems is obtained.In this model,the decision rules of pessimists,neutrals,and optimists are discussed.On this basis,a novel attribute certainty degree is defined for the attribute selection.Thus,a novel sequential three-way decision method is constructed in incomplete information systems.The method is verified by a medical diagnosis example.Secondly,in intuitionistic fuzzy information systems,intuitionistic fuzzy conditional probability and their corresponding properties are discussed.Combining the intuitionistic fuzzy conditional probability and the principle of minimum losses,a three-way decision theory of minimum losses based on intuitionistic fuzzy numbers is proposed.Then,using the attribute significance degree,a sequential three-way decision method based on intuitionistic fuzzy numbers is constructed.And the method is verified by an example.Finally,combining the intuitionistic fuzzy conditional probability and the principle of maximum profits,a two-state maximum profit three-way decision method of intuitionistic fuzzy information systems is proposed,and then it is compared with the minimum loss three-way decision method of intuitionistic fuzzy information systems.Besides,on the basis of descriptions of membership and non-membership,adding a description of hesitation,a three-state maximum profit three-way decision method of intuitionistic fuzzy information systems is studied.