On priority weights and consistency for incomplete hesitant fuzzy preference relations

The hesitant fuzzy preference relation (HFPR) is a useful tool for decision makers to elicit their preference information over a set of alternatives. In this paper, it is first proposed an approach to deriving a priority weight vector from an incomplete HFPR using the logarithmic least squares method. Based on the priority weight vector, the consistency index of an incomplete HFPR is defined, which calculates the average deviation between the priority weight vector and all elements of the incomplete HFPR. For an incomplete HFPR which is unacceptably consistent, an automatic algorithm is developed to improve the consistency. These results are then extended to propose a new procedure for group analytic hierarchy process to deal with multi-criteria group decision making problems. The feasibility and effectiveness of the proposed approaches are demonstrated by some numerical examples.