Quantum Representation of Basic Probability Assignments Based on Mixed Quantum States

Understanding the uncertainty is a very important issue in Dempster-Shafer theory (DST) for modelling and fusing uncertain information. In traditional views, the uncertainty involved in a basic probability assignment (BPA) of DST is interpreted in many ways, including intervals of probabilities, non-additive probabilities, degrees of belief, random sets, etc. In this paper, the idea of quantum is imported in DST to interpret the origin of uncertainty in a BPA. Within the study, a novel scheme is proposed to implement the quantum representation of BPA. And several important concepts, including degree of quantum effect, generation of belief and plausibility measures based on BPA’s quantum representation, quantum entropy and observed entropy of a BPA, as well as their properties, are also investigated. The study provides a new viewpoint to understand the uncertainty involved in a BPA and interpret the BPA. Numerical examples and analysis about the quantum representation of BPA are given to illustrate the study.