Interval Valued Intuitionistic Fuzzy Probabilistic Rough Set Model And Its Application

Because of the lower and upper approximation of the classical rough sets is too harsh to defined,the value of the boundary domain is relatively less,which is not conducive to the choice of the decision scheme.In order to solve this problem,the researchers add the probability threshold to the classical rough set theory,and propose the probability of the probability rough set.The main work of this paper is to extend the probabilistic rough set model and discuss the interval intuitionistic fuzzy information system on the basis of probabilistic rough sets.The main purpose is to make a decision by establishing an interval intuitionistic fuzzy probability rough set model,mainly from the following aspects.Firstly,the division operation of interval intuitionistic fuzzy number is defined reasonably,and on this basis,the formula of conditional probability based on interval intuitionistic fuzzy probability space is proposed.The division operation of interval intuitionistic fuzzy number is still blank in the existing literature.Based on the requirement of conditional probability,this paper reasonably defines the division of two interval intuitionistic fuzzy numbers,so that it is finished in space.In addition,the four operations of interval intuitionistic fuzzy numbers are effectively supplemented.On this basis,the formula of conditional probability in interval intuitionistic fuzzy probability space is given by using Bayes formula,which is the basis for extending the model of subsequent probabilistic rough sets.What’s more,the probabilistic rough set model is generalized to the interval intuitionistic fuzzy probability space,and the interval intuitionistic fuzzy probability rough set model is constructed.The model is based on the interval intuitionistic fuzzy probability approximation space,based on the interval intuitionistic fuzzy event set and the interval intuitionistic fuzzy equivalence relation,and the interval intuitionistic fuzzy sets are defined on the upper and lower threshold of the probability threshold,by defining the interval intuitionistic fuzzy equivalence class.A new decision model is constructed to solve inexact,incomplete and inconsistent information,and then the basic properties of the new model are discussed,and the properties and theorems of the new model are given.Finally,the loss function is introduced to give the expression of the probability threshold of the new model.By calculating the loss function which is based on the interval intuitionistic fuzzy number,the expression of the probability threshold of the new model is determined,and the decision rule which is based on the probability threshold is given.In addition,the feasibility of the example is given to verify the feasibility of the model.