A new ordinal-cardinal consensus reaching method for multi-attribute group decision-making considering individual belief transformation

Individual beliefs dynamically transform during negotiation and interaction in the consensus reaching process (CRP), influencing preference formation and posing significant challenges to group decision-making methods. In this paper, we develop a method for multi-attribute group decision-making (MAGDM) that incorporates individual belief transformation from the ordinal and cardinal perspectives. First, we gather two types of preference information from individuals: pairwise comparison relationship and alternative-attribute evaluation information. To preserve as much original preference information as possible, we propose verification and adjustment models that consider consistent attribute prioritization to obtain consistent preference information. On this basis, an optimization model that minimizes bias variables is developed to obtain the individual alternative ranking results. Subsequently, an ordinal-cardinal consensus feedback adjustment mechanism is designed to refine the adjusted preference information of individuals following the attainment of group consensus in the CRP. This mechanism employs quantum probability theory (QPT) to effectively model belief transformation occurring during interpersonal interactions. Additionally, a maximum support degree model is proposed to obtain the final group alternative ranking result. Finally, a case study involving healthcare workers and patient sharing decision-making is illustrated, providing invaluable insights into the practicality and acceptability of drug treatment selection solutions within real-world contexts. This analysis aims to inform future advancements in shared decision-making practices.