Belief Evolution Network: Probability Transformation of Basic Belief Assignment and Fusion Conflict Probability

We give a new interpretation of basic belief assignment transformation into probability distribution, and use directed acyclic network called belief evolution network to describe the causality between the focal elements of a BBA. On this basis, a new probability transformations method called full causality probability transformation is proposed, and this method is superior to all previous method after verification from the process and the result. In addition, using this method combined with disjunctive combination rule, we propose a new probabilistic combination rule called disjunctive transformation combination rule. It has an excellent ability to merge conflicts and an interesting pseudo-Matthew effect, which offer a new idea to information fusion besides the combination rule of Dempster.

Quantum belief function

The belief function in Dempster Shafer evidence theory can express more information than the traditional Bayesian distribution. It is widely used in approximate reasoning, decision-making and information fusion. However, its power exponential explosion characteristics leads to the extremely high computational complexity when handling large amounts of elements in classic computers. In order to solve the problem, we encode the basic belief assignment (BBA) into quantum states, which makes each qubit correspond to control an element. Besides the high efficiency, this quantum expression is very conducive to measure the similarity between two BBAs, and the measuring quantum algorithm we come up with has exponential acceleration theoretically compared to the corresponding classical algorithm. In addition, we simulate our quantum version of BBA on Qiskit platform, which ensures the rationality of our algorithm experimentally. We believe our results will shed some light on utilizing the characteristic of quantum computation to handle belief function more conveniently.