A distribution linguistic group decision-making method considering twin multiplicative data envelopment analysis regret-rejoice cross-efficiency

Traditional approaches to group decision-making (GDM) often assume that decision-makers (DMs) are perfectly rational, which neglects the psychological attitudes exhibited by DMs during the decision-making process. To address this issue, this paper designs a novel method for GDM with multiplicative distribution linguistic preference relations (MDLPRs), which incorporates twin multiplicative data envelopment analysis (TMDEA) regretrejoice cross-efficiency models and a weighting model with individual tolerance. Firstly, we provide a clear definition of MDLPRs based on multiplicative linguistic terms that capture the asymmetrical qualitative recognition of DMs. Then, a weighting model is constructed to obtain DM's weights. This model assumes that DMs are boundedly rational and have a certain tolerance level for group consensus measurement. Subsequently, TMDEA cross-efficiency models are developed based on different perspectives. On this basis, we further propose TMDEA regret-rejoice cross-efficiency models that consider the psychological risks of DMs. Furthermore, the method for GDM based on TMDEA regret-rejoice cross-efficiency models and individual tolerance with MDLPRs is given. Finally, we present a case study of the selection of the Ya'an ecological monitoring station in China to test the validity and applicability of the proposed method. The merits and robustness of the constructed method are highlighted by sensitive analysis and comparative analysis.