A novel quantum model of mass function for uncertain information fusion

Understanding the uncertainty involved in a mass function is a central issue in Dempster–Shafer evidence theory for uncertain information fusion. Recent advances suggest to interpret the mass function from a view of quantum theory. However, existing studies do not truly implement the quantization of evidence. In order to solve the problem, a usable quantization scheme for mass function is studied in this paper. At first, a novel quantum model of mass function is proposed, which effectively embodies the principle of quantum superposition. Then, a quantum averaging operator is designed to obtain the quantum average of evidence, which not only retains many basic properties, for example idempotency, commutativity, and quasi-associativity, required by a rational approach for uncertain information fusion, but also yields some new characters, namely nonlinearity and globality, caused by the quantization of mass functions. At last, based on the quantum averaging operator, a new rule called quantum average combination rule is developed for the fusion of multiple pieces of evidence, which is compared with other representative average-based combination methods to show its performance. Numerical examples and applications for classification tasks are provided to demonstrate the effectiveness of the proposed quantum model, averaging operator, and combination rule.