Three-Way Decision Method Based On Intuitionistic Fuzzy Information

With the explosive growth of information in the real world,the presentation of information is becoming more and more diverse.Among them,uncertain information has received wide attention.As a mathematical tool to describe uncertain information,intuitionistic fuzzy sets can describe the three elements of affirmation,hesitation and negation of information.It can reflect the thought of ”three parts and governance”.Similarly,three-way decision theory is also can reflect this idea.It gives three different choices of decision-making: support,hesitation and rejection.In the intuitionistic fuzzy information system,the application of three-way decision theory has made great achievements.However,it lacks in the exploration of dominance relationship and the construction of intuitionistic fuzzy shadow sets.In view of the above problems,this paper has done the following research:(1)To deal with the problems of too strict requirements for the existing intuitionistic fuzzy dominance relationship,large loss of evaluation information and incomplete utilization,an intuitionistic fuzzy perturbation dominance relationship in line with the characteristics of intuitionistic fuzzy is proposed by using the disturbance degree between intuitionistic fuzzy sets.And then a perturbation dominance class with lower requirements than the equivalence class is obtained.The related properties of dominant classes are discussed.(2)Aiming at the problem that the conditional probability in the existing intuitionistic fuzzy three branch decision-making method is expressed by real numbers,which leads to the loss of uncertain information,a calculation method of conditional probability expressed by intuitionistic fuzzy numbers is proposed based on the perturbation dominance relationship,and the three-way decision and multi-attribute decision-making rules are given.Then,an example is given to verify the effectiveness of the method.And the sensitivity of the dominance degree and risk avoidance coefficient is analyzed.(3)Based on intuitionistic fuzzy membership function and non-membership function,a new intuitionistic fuzzy shadow set model is proposed.Combining it with the three-way decision theory,the corresponding decision rules are given.Then the three-way decision-making rules are discussed in terms of optimism and pessimism.And the threshold function and its calculation method are given.In practical applications,the time cost of decision-making needs to be considered.Therefore,the value range of the threshold function is constrained accordingly.The sufficient conditions and the necessary conditions for accepting and rejecting decisions are successfully obtained.Finally,an example is given to verify the rationality of the model.