A Quantum Graph Model for Conflict Resolution Considering Decision-Makers’ Risk Attitudes Based on Interval-Valued Intuitionistic Fuzzy Preferences with Application to Doctor-Patient Disputes

Doctor–patient disputes are harmful because they can foster social tension, trigger public distrust of the healthcare providers and the system, and affect the image of the medical industry itself. This inherently complex decision-making environment is exacerbated by, on the one hand, the uncertainty and risk attitudes of various decision-makers (DMs), and on the other, the superposition and interference of composite DMs (CDMs) composed of various single DMs. Although the traditional graph model for conflict resolution (GMCR) can be applied to doctor–patient disputes, it struggles with such complex, uncertain situations and the potential for differing opinions within these groups, making it difficult to reach a consensus and provide reasonable solutions. Moreover, negotiation in GMCR follows the classical probability theory based on Boolean logic, which implies compatibility of states, an absence of order effects, and thus deviation in group decision results. Therefore, this study introduces quantum theory into the GMCR to explain and simulate human thinking. Specifically, interval-valued intuitionistic fuzzy preferences (IVIFPRs) are first used to show DMs’ uncertainty preferences in the quantum GMCR (QGMCR). Next is to fully consider the differentiated risk attitude and irrational psychological behavior of different experts in CDMs for constructing a novel preference ranking method. Among them, a new score function is proposed to deduce the interference entanglement behavior of DMs by applying the principles of quantum probability theory. Furthermore, this paper constructs quantum stability in QGMCR to describe interest and strategy interaction among DMs or CDMs in uncertainty environments. Finally, considering the scarcity of medical resources, heavy economic burden, and low social trust in developing countries, doctor–patient disputes are more likely to trigger social unrest and trust crises, thereby affecting the overall stability and development of society. Resolving doctor–patient disputes not only illustrates the practicality of QGMCR but also provides policy suggestions for building a harmonious society for managers. In conclusion, this study characterizes the ambiguity and risk attitude of CDMs, proposes a feasible preference ranking acquisition method for CDMs, and designs a new set of quantum stability definitions, which provides a reliable analytical tool for resolving doctor–patient disputes.