A decision support model for group decision making with hesitant multiplicative preference relations

The hesitant fuzzy preference relation (HFPR) was recently introduced by Zhu and Xu to allow the decision makers (DMs) to offer several possible preference values over two alternatives. In this paper, we use an asymmetrical scale (Saaty's 1-9 scale) to express the decision makers' preference information instead of the symmetrical scale that is found in a HFPR, and we introduce a new preference structure that is known as the hesitant multiplicative preference relation (HMPR). Each element of the HMPR is characterized by several possible preference values from the closed interval [1/9, 9]; thus, it can model decision makers' hesitation more accurately and reflect people's intuitions more objectively. Furthermore, we develop a consistency- and consensus-based decision support model for group decision making (GDM) with hesitant multiplicative preference relations (HMPRs). In this model, an individual consistency index is defined to measure the degree of deviation between an HMPR and its consistent HMPR, and a consistency improving process is designed to convert an unacceptably consistent HMPR to an acceptably consistent HMPR. Additionally, a group consensus index is introduced to measure the degree of deviation between the individual HMPRs and the group HMPR, and a consensus-reaching process is provided to help the individual HMPRs achieve a predefined consensus level. Finally, a numerical example is provided to demonstrate the practicality and effectiveness of the developed model.