A multi-attribute group decision-making model in social networks under quantum framework

Purpose Many studies on multi-attribute group decision-making (MAGDM) assume decision-makers (DMs) act independently. But often DMs maybe interact or interfere with each other. With the rise of social networks, the concept of interference effects has transitioned from an abstract notion in quantum theory to a tangible phenomenon. Therefore, this paper aims to elicit reliable parameters of interference effects from the social relationships among DMs. Design/methodology/approach Quantum probability theory (QPT) offers a framework for simulating the cognition and behavior of DMs and modeling the interference effects in quantum theory. Therefore, this paper develops an interaction-based MAGDM model within a quantum context. To capture individual diversity and uncertainty, individual preference is presented as state probabilities of alternatives in the form of probability linguistic variables and group preference is formulated through QPT methodologies. Additionally, the Shapley value and interaction index obtained from a linear programming model that reflects the interference effects between DMs are introduced into the quantum framework. Findings A numerical example is presented. And through comparative analysis, we find that, by employing QPT to robustly account for interference effects and innovatively using an interaction index based on a fuzzy measure to represent the cosine of phase differences, bypassing the need for prior knowledge, the model is more aligned with real-world group decision-making complexities. Originality/value This paper establishes a connection between interference effects and non-additive measures, offering fresh insights into addressing the MAGDM problem within a quantum framework considering interference effects.