Hesitant multiplicative best and worst method for multi-criteria group decision making

Abstract

Best-worst method (BWM) has been extended in various uncertain scenarios owing to fewer comparisons and better reliability. This article utilizes hesitant multiplicative (HM) sets (HMSs) to express reference comparisons (RCs) and develops a novel HM BWM (HMBWM). We first define the multiplicative consistency for HM preference relation (HMPR). A fast and effective approach is designed to derive the priority weights (PWs) from an HMPR. To extend BW into HMPR, the score value of each criterion is computed to identify the best and worst criteria. Then, the PWs are acquired through constructing a 0–1 mixed goal programming model based on the HM RCs (HMRCs). The consistency ratio is given to judge the multiplicative consistency of HMRCs. An approach is proposed to enhance the consistency when the HMRCs are unacceptably consistent. Thereby, a novel HMBWM is proposed. On basis of HMBWM, this article further develops a novel method for group decision making (GDM) with HMPRs. The decision makers’ weights are determined by consistency ratio and the group PWs of alternatives are obtained by minimum relative entropy model. Four examples show that HMBWM possesses higher consistency and the proposed GDM method has stronger distinguishing ability, less computation workload and fewer modifications of elements.