Priority weights acquisition of linear uncertain preference relations and its application in the ranking of online shopping platforms

The linear uncertain preference relations (LUPRs) uses an uncertain variable to represent the decision-maker’s pairwise comparison judgment of the scheme. The variable is subject to the linear uncertain distribution, which is the extension of the traditional fuzzy preference relations (FPRs) and interval fuzzy preference relations (IFPRs). This paper proposes a group decision modeling problem, constructs the priority weights acquisition models of the additively and multiplicatively consistent LUPRs, and especially solves the problem that the weight solution is negative value or no solution by using traditional methods to acquire weights in consistent FPRs and IFPRs. Based on these two types of consistent structure of LUPRs, this study constructs the crisp number, interval number weight solving models of LUPRs and the group decision ranking models with LUPRs. The results show that these new models are suitable for solving the weight vector of traditional FPRs and IFPRs. The case of online shopping platform selection compares the results obtained by various methods of calculating weights, further illustrating the effectiveness and rationality of the new methods.