A quantum framework for modelling subjectivity in multi-attribute group decision making

Due to the increasing complexity of decision tasks, the experiences, knowledge or opinions from multiple decision makers (DMs) often need to be aggregated. Many multi-attribute group decision making (MAGDM) approaches have been widely studied. In a MAGDM problem, the multiple DMs are usually regarded as independent. However, in many practical situations, the opinions from different DMs are likely to influence each other or to be affected by the environment. To address it, a quantum framework based on quantum probability theory is proposed in this paper. The goal is to model the subjectivity in MAGDM when we have subjective beliefs towards DMs' independence or relations. The modeled subjectivity sources from the interference of beliefs. However, in classical models, subjectivity usually comes from the preference of DMs when determining weights or giving an evaluation towards alternatives. In this paper, the classical MAGDM technics are used to do the preparation firstly. Then a Bayesian network is constructed and it is extended to a quantum framework. The beliefs toward DMs are in a superposition. Namely, the opinions of DMs are viewed as various wave functions that are occurring at the same time. Then the beliefs will interfere with each and influence the final result. When all the DMs are deemed independent, the quantum framework will degenerate into a classical Bayesian network. The various cases of a simple example have been discussed and analyzed. A real supplier section problem is also used to illustrate and validate our model. Finally, an overall comparative analysis regarding the subjectivity in MAGDM is performed.