Application of quantum-like Bayesian network and belief entropy for interference effect in multi-attribute decision making problem

Abstract

Multi-attribute decision making (MADM) is a classical model that widely used in various fields. But most research about this topic often assume that the attributes are independent each other. In fact the attributes maybe interact or interference each other in many cases. There are researches on the interact relationships with Choquet integral, but there is no research on the interference effect by far to the authors. In this paper, a multi-attribute decision-making model is proposed by considering the interference effects between attributes with quantum-like Bayesian network (QLBN) and belief entropy. Quantum probability theory (QPT) is more in line with people's thinking by considering the interference relationships between attributes, which is represented as the interference value in quantum theory. Belief entropy, an index to calculate the uncertainty of probability, is introduced as a method to calculate the interference value in this paper. Finally, the model is applied to assessing the industrial economic benefit as well as the quantitative performance comparison between the traditional probability and the QLBN probability is presented. It shows that the combination of QLBN model and belief entropy has prediction ability compared with the traditional Bayesian network model.