A Novel Consensus-Based Group Decision-Making with Dual Probabilistic Linguistic Preference Relations and Its Application in Green Battery Supplier Selection

Dual probabilistic linguistic preference relations (DPLPRs) effectively capture diverse preferences of decision-makers (DMs) by considering both membership degree (MD) along with non-membership degree (NMD) for various evaluation criteria. The introduction of group consensus mechanism can effectively coordinate the differences in opinions among different DMs, thereby making the decision results more reliable. The selection of a green battery supplier (GBS) involves assessing and choosing environmentally sustainable battery suppliers amid numerous complex and uncertain factors, which complicates the evaluation process. This paper studies a consensus-based group decision-making (GDM) method utilizing DPLPRs and applies it to the critical problem of GBS selection. First, multiplicative consistency is defined for DPLPRs. A convergent local consistency improvement algorithm is proposed, which adjusts the DPLPR from unacceptable multiplicative consistency to acceptable multiplicative consistency while maintaining the original evaluation information at the greatest extent. Second, the similarity measure and group consensus measure for DPLPRs are expressed. On this basis, a convergent consensus reaching strategy is designed. The developed algorithm iteratively modifies the DPLPRs exhibiting the lowest alignment with others, guiding the group toward a consensus over time. Finally, by integrating the consistency improvement algorithm and the consensus reaching strategy, a GDM with DPLPRs is proposed. Its effectiveness in the selection of GBS is analyzed, and compared with other existing approaches.