A new linear programming model and its properties for deriving strict interval priority vectors of interval fuzzy preference relation

Fuzzy preference relation is a popular and powerful tool to express decision maker´s views. Due to the complexity and uncertainty of problems, the input information arguments provided by decision makers are given in the form of interval numerical values rather than the exact values. Based on multiplicative consistent interval fuzzy preference relation, we give the definitions of the largest range priority vector (LRPV) and strict priority vector of interval fuzzy preference relation. We give a sufficient and necessary condition to judge whether a priority vector is strict or not. Furthermore, we construct the linear programming model by maximizing the sum of radius of interval number to derive strict interval priority vector for interval fuzzy preference relation more easily than LPRV method. We also discuss the special case in which changed constraints can make interval weights in the strict interval priority vector have less radius, which are included in that of interval priority vector by LRPV method. Finally, we give the numerical example to show that the model is more convenient for the decision-maker to obtain the priority vector and also verifies results in this paper.