Quantum X-entropy in generalized quantum evidence theory

Abstract

Generalized quantum evidence theory (GQET) is effective for uncertainty reasoning from the view of the quantum framework in an open world. However, how to construct the quantum model of GQET to bridge evidence theory and quantum theory remains an open issue. In this paper, a new quantum model of GQET is proposed, which provides a new perspective to express and handle the generalized quantum mass function with more explicit physical meanings. Specifically, a new quantum model for the generalized quantum mass function in GQET is first proposed, which represents the generalized quantum mass function as a mixed quantum system of quantum pure states. In addition, belief and plausibility measurement functions are newly defined in terms of the generalized quantum mass function in GQET, which represent the upper and lower bounds to support decision-making by means of the new quantum model. In addition, a new quantum X-entropy is proposed to measure the uncertainty of the generalized quantum mass function in GQET. The proposed quantum X-entropy can be viewed as the generalized model of classical von Neumann entropy. In particular, when the basic belief amplitude assignment of a GQBBA is in accordance with a probability distribution, quantum X-entropy degenerates into von Neumann entropy. Numerical examples demonstrate the effectiveness of the new quantum model of GQET as well as quantum X-entropy.