An extension of multi-attribute group decision making method based on quantum-like Bayesian network considering the interference of beliefs

Abstract

Multi-attribute group decision making (MAGDM) problem has become one of the most remarkable topics recently. MAGDM is made up of multiple decision makers (DMs) who perform opinions on a set of alternatives and then choose the appropriate one. In the classical decision-making process, the multiple DMs are usually regarded as independent and the opinions usually come from the preference of DMs when determining weights of attributes or giving evaluation of alternatives. However, MAGDM is a complicated cognitive process that involves the diverse and uncertainty cognition of DMs from different backgrounds and fields, and the opinions from DMs are likely to interfere with each other. This paper proposes an extension method based on quantum-like Bayesian network (QLBN) and belief entropy considering the interference of beliefs on the basis of our previous research. The purpose is to model subjectivity sourced from the interference of DMs’ beliefs at different decision-making stages, including the aggregation of attributes probabilities and alternatives probabilities. In this paper, a QLBN for MAGDM problem is constructed firstly. The beliefs of DMs are in a superposition state in it, that is, the opinions of DMs are regarded as wave functions occurring in QLBN. Then the probabilities of attributes and the probabilities of alternatives in QLBN are aggregated across all DMs, and the alternatives are sorted. In the process of aggregation, the beliefs from different DMs will interfere with each other. Belief entropy, an index to calculate the uncertainty of probability is introduced to calculate the interference value. When the interference between DMs is considered only in a certain decision-making stage, the proposed method will degenerate into the existing QLBN methods; and when all DMs are regarded as independent, the QLBN will degenerate into a classical BN. Finally, a supplier selection problem is introduced to illustrate and validate our model. The comparison analyses show that the proposed approach can fully consider the interference between DMs and the ranking result are more reasonable and realistic.