Belief Entropy-Based MAGDM Algorithm Under Double Hierarchy Quantum-like Bayesian Networks and Its Application to Wastewater Reuse

The traditional multi-attribute group decision-making (MAGDM) method easily ignores the interference effect among decision-makers (DMs), while quantum theory can effectively portray the uncertainty in the decision-making process and quantify the preference interference among DMs. The asymmetry of evaluation information in social networks can have a significant impact on decision-making. In this paper, a quantum MAGDM algorithm based on probabilistic linguistic term sets (PLTSs) and a quantum-like Bayesian network (QLBN) is proposed (PL-QLBN), utilizing quantum theory and social network concepts and introducing a novel method for calculating interference effects based on belief entropy. Firstly, a complete trust network is constructed based on the probabilistic linguistic trust transfer operator and the minimum path method. A trust aggregation method, considering interference effects, is proposed for the QLBN to determine the DM weights. Next, the attribute weights are calculated based on the entropy weight method. Then, a probabilistic linguistic MAGDM considering interference effects is proposed based on the QLBN. Finally, the feasibility and validity of the provided method are verified through Hefei City’s selection of wastewater reuse alternatives.