Deriving the priority weights from incomplete hesitant fuzzy preference relations in group decision making

The concept of hesitant fuzzy preference relation (HFPR) has been recently introduced to allow the decision makers (DMs) to provide several possible preference values over two alternatives. This paper introduces a new type of fuzzy preference structure, called incomplete HFPRs, to describe hesitant and incomplete evaluation information in the group decision making (GDM) process. Furthermore, we define the concept of multiplicative consistency incomplete HFPR and additive consistency incomplete HFPR, and then propose two goal programming models to derive the priority weights from an incomplete HFPR based on multiplicative consistency and additive consistency respectively. These two goal programming models are also extended to obtain the collective priority vector of several incomplete HFPRs. Finally, a numerical example and a practical application in strategy initiatives are provided to illustrate the validity and applicability of the proposed models.