A Study On Linear Uncertainty Preference Relationship And Consistency Under Incomplete Information

In the 5G era and the background of big data,large-scale and large-scale group decision-making(GDM),the speed of information derivation,duplication,and diffusion has increased exponentially.In order to make full use of information to solve problems such as GDM,consensus,and ranking,experts often use fuzzy numbers,intervals,hesitant,intuitionistic and other heterogeneous fuzzy preference relations for decision-making analysis.However,the interval fuzzy preference relation(IFPR)has the disadvantages of not considering the interval distribution,and the interval cannot be regarded as a whole to participate in the operation,which is easy to cause the discretization of information,and the information cannot be fully utilized.However,uncertainty theory fits the decision maker's preference information with uncertain variables that obey different distributions,and uses belief degree and the inverse distribution of the variables for calculations,which can use the information as a whole.Therefore,this paper combines uncertainty theory with fuzzy preference relation(FPR)and IFPR,then proposes linear uncertain preference relation(LUPR)and its theoretical framework:(1)Based on uncertainty theory and IFPR,this paper regards interval elements as uncertain variables which subject to linear uncertainty distribution,and proposes LUPR,then the additive consistency and multiplicative consistency definitions for LUPR are given.By comparing with traditional FPR and IFPR,it can be concluded that LUPR is a further extension of FPR and IFPR.After analyzing the characteristics of FPR,IFPR,UPR and LUPR,this paper gives the inclusion relation,transformation method,advantages and disadvantages comparison of the four preference relations.(2)Based on the additive consistency and multiplicative consistency definitions of LUPR,this paper proposes complete models and consistent algorithms for incomplete LUPR,which obtains the analytical expression of incomplete value.This method is also suitable for information completion problem under different uncertainty distribution forms and different belief degree.The effectiveness and rationality of the method are verified by the case of disaster assessment.(3)In order to solve the problem that there is no solution or negative value of weight vector in traditional FPR and IFPR,this paper improves the relationship between judgment element and weight,and constructs crisp number and interval number weight vector solving models of LUPR,which is also suitable for solving weight vector of FPR and IFPR.The selection and ranking of online shopping platform prove the rationality and effectiveness of the method.The LUPR and its additive and multiplicative consistency theoretical framework proposed in this paper further enrich the content of heterogeneous fuzzy preference relations,which is suitable for GDM,ranking and other problems in uncertain environment.