A consensus algorithm based on the worst consistency index of hesitant fuzzy preference relations in group decision-making

This paper mainly solves the individual consistency and group consensus in the decision-making with hesitant fuzzy preference relations (HFPRs). The worst consistency index (WCI) is used to measure the individual consistency level. The envelop of an HFPR called envelop of HFPR (EHFRP) is proposed in the consensus reaching process (CRP). Two algorithms are proposed: one is to improve the WCI, in which only one pair of elements are revised in the consistency improving process each time, which aims to preserve the decision makers' (DMs') original information as much as possible. Another algorithm is proposed to improve the consensus in the CRP. To aggregate individual EHFPRs into one group HFPR, a new induced ordered weighted averaging (IOWA) operator is presented, called envelope HFPR-IOWA (EHFPR-IOWA), which allows the experts' preference to be aggregated in such a way that the most consistent ones are given more weight. Finally, an illustrative example and comparisons with the existing methods are provided to show the effectiveness of the proposed method.