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1. chinaXiv:202103.00132 [pdf]

CET: A New Complex Evidence Theory

Lipeng Pan; Yong Deng
Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

" Dempster-Shafer evidence theory, as an extension of Probability theory, is widely used in the field of information fusion due to it satisfies weaker conditions than probability theory in dealing with uncertain information. Nevertheless , the description space of the current evidence theory is only a real space, and it cannot effectively describe and process the uncertain information in the face of multidimensional characteristic data and periodic data with phase angle changes. Based on this gap , in this paper, Dempster-Shafer evidence theory is extended to the complex Dempster-Shafer evidence theory. In complex Dempster-Shafer evidence theory, mass function that used to describe the uncertain information extends from the real space to the complex space, named as complex mass function, and the modulus of the mass function indicates the degree of support for the proposition. On this basis, other basic concepts used to describe uncertainty information are also defined and discussed, such as complex belief function, complex plausibility function, etc. In order to perfect the complex Dempster-Shafer evidence theory, the complex Dempster combination rule (CDCR) is supplemented. CDCR is an extension of Dempster combination rule (CDR), which satisfies the commutative and associative laws just as CDR does, and it can degenerate into CDR under certain condition. In addition, we propose a method to generate complex mass function and apply it to target recognition. The recognized results show that compared with the mass function of the real plane, the target recognition rate can be larger by using complex mass function to describe the uncertain information.

submitted time 2021-03-23 Hits370Downloads255 Comment 0

2. chinaXiv:202102.00030 [pdf]

A new entropy measure of quantum system uncertainty

Yige Xue; Yong Deng
Subjects: Physics >> General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

Quantum theory is currently the most important research field. Before processing the information of a quantum system, we must first understand how to measure the uncertainty of a quantum system. Von Neumann entropy is a very classic method to measure the uncertainty of quantum systems. However, due to the particularity of quantum systems, it is very difficult to measure the uncertainty of quantum systems, so that the measurement efficiency of the classical von Neumann entropy is not high in some cases. Based on the classic von Neumann entropy and belief entropy, this paper proposes a new entropy model to measure the uncertainty of quantum systems, which can use fully the eigenvalues and eigenvectors of the density matrix of quantum systems, and give the uncertainty of the quantum system. Some numerical examples are used to prove that the proposed entropy is more efficient and reliable in measuring quantum systems than the classical von Neumann entropy. The experimental results show that the proposed entropy can measure the uncertainty of quantum systems more efficiently and reliably than the classical von Neumann entropy.

submitted time 2021-02-04 Hits1243Downloads380 Comment 0

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