Some linear programming models for obtaining the priority vector of interval multiplicative preference relations

Interval multiplicative preference relation is very useful in expressing decision makerpsilas preferences on alternatives under uncertain preference information. How to derive priorities from a interval multiplicative preference relation is an interesting and important issue in decision making. In this paper, we first define the concepts of interval multiplicative preference relations, consistent interval multiplicative preference relations, and then propose some simple and practical linear programming models, based on consistent interval multiplicative preference relations for obtaining the priority vector of interval multiplicative preference relations.These linear programming models are also extended to obtain the collective priority vector of several interval multiplicative preference relations. Finally, the proposed models are tested and examined with two numerical examples and prove to be simple, effective and practical.