Feifei Jin

The Markov decision process (MDP) provides a framework for sequential decision optimization under uncertainty and serves as a foundation for dynamic programming problems. However, current robust optimization approaches often overlook the social attributes of decision-makers (DMs), while behavioral models that do account for social factors often treat them as external constraints rather than integrating them into a distributionally robust optimization (DRO) framework. To address these challenges, we construct a distributionally robust Markov decision process (DRMDP) that integrates empathetic relationships, aiming to minimize the system’s total cost while also improving decision-making stability. First, we model DM profiles and the dynamic evolution of a group trust network to capture the effects of subjective performance evaluation. Next, we establish a principled learning process to generate a global empathetic weight matrix. Then, we construct a psychological cost mechanism that quantifies deviations from group consensus and trades off economic objectives against social alignment. Subsequently, we design an improved DRO process to analyze the stability of the MDP under empathetic relationships. Finally, experiments reveal a synergistic effect: the empathetic mechanism mitigates the conservatism of pure robust strategies, leading to a substantial reduction in both average total cost and cost dispersion. These findings demonstrate that high-quality group consensus can complement the data-derived robustness, enhancing both economic efficiency and decision stability.

Dual probabilistic linguistic preference relations (DPLPRs) effectively capture diverse preferences of decision-makers (DMs) by considering both membership degree (MD) along with nonmembership degree (NMD) for various evaluation criteria. The introduction of a 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 to 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.

With the rapid evolution of digital trade, the cross-border e-commerce industry is undergoing significant transformation, necessitating a comprehensive upgrade in supply chain management. Evaluating supply chain efficiency becomes crucial amidst this backdrop. This process can be seen as a multi-attribute group decision-making (MAGDM) problem involving different evaluation attributes. However, there are some shortcomings of existing MAGDM methods, such as the imperfect method of solving attribute weight vectors, and the uncertainty of input–output data are not considered. Therefore, based on the Case-based Reasoning Method (CBR) and interval DEA model, this paper designs an interval-valued probabilistic linguistic MAGDM method with prospect theory. In the process of calculating the attributes’ weight vector, we first compute the prospect values of Interval-valued probabilistic linguistic term sets (IVPLTSs). Then, the CBR and linear programming model are developed to classify the decision-making units (DMUs). Additionally, we integrate interval data envelopment analysis (DEA) for efficiency evaluation, and an optimization model is devised for efficiency correction. Moreover, the constructed method is applied to evaluate the supply chain management efficiency of eight listed global e-commerce firms and compare it with other MAGDM methods. The results show that our method considers the bounded rationality of decision makers, and the improved efficiency evaluation model makes the evaluation process more methodical and justifiable.