A trust-based quantum probabilistic linguistic multi-criteria group decision making model considering interference effect

Abstract

In group decision-making (GDM), there exist cognitive and realistic uncertainties and humans exhibit hesitation and ambiguity. Using probabilistic linguistic term sets (PLTSs) can better adapt to the above challenges. However, the current PLTS-based methods rarely take the subjectivity and behavior of experts into account, especially the influence of trust relations and subjective beliefs. This paper combines the trust network and the quantum probability theory (QPT) in GDM, and proposes a new probabilistic linguistic multi-criteria group decision-making (MCGDM) model considering the trust relationships and the interference effects between experts. Firstly, probabilistic linguistic evaluations and trust information are collected. Then, the entropy-weight method based on PLTS is proposed to determine criterion weights. A new mixed multi-path trust transfer aggregation operator that integrates both the path length and the path quality is defined, to establish a complete trust network and measure the expert weight. Thirdly, because of the certain interference between experts, a quantum-like Bayesian network framework is built to aggregate the opinions of experts. During the process, the system is in a superposition state, and personal opinions are regarded as interfering wave functions, affecting the final results. Finally, an example of the prevention and control of COVID-19 in a city is used for verification and sensitivity and comparison analyses are provided to verify the effectiveness of the method.