Multi-attribute quantum group interference decision model considering minimum constraint and information entropy

Abstract

About multi-attribute group decision making process, the opinions of different decisions will interfere with each other, or be affected by the decision-making environment, resulting in an unobserved interference effect, which is regarded as quantum entanglement in quantum theory. In this paper, an interference effect model based on minimum constraint and information entropy is proposed to measure the interference value in quantum decision models. Firstly, considering the interference effects of decision makers’ opinions, the evaluation opinions of decision makers are aggregated using Quantum-like Bayesian Network (QLBN), which are regarded as wave functions superimposed in the quantum model. Secondly, due to the uncertainty of decision process, information entropy and minimum constraint are combined to solve the interference effect. The minimum constraint is used to limit the range of interference values and the information entropy represents the uncertainty in the decision process. The grey relational degree represents the conditional probability of the decision maker about the alternatives. Thirdly, the weights of attributes and the probabilities of the alternatives are aggregated about decision makers by the proposed interference effect model, and then the alternatives are ranked by the aggregated probabilities. Subsequently, a numerical example is used to verify the validity and rationality of the model. Comparative analyses and sensitivity analyses are also implemented to demonstrate the stability and reliability of our method.