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1. chinaXiv:202106.00009 [pdf]

Complex-valued Deng Entropy

Lipeng Pan; Yong Deng
Subjects: Computer Science >> Other Disciplines of Computer Science

Complex evidence theory has been applied to several fields due to its advantages in modeling and processing uncertain information. However,to measure the uncertainty of the complex mass function is still an open issue. The main contribution of this paper is to propose a complex-valued Deng entropy. The complex-valued Deng entropy can effectively measure the uncertainty of the mass function in the complex-valued framework. Meanwhile, the complex-valued Deng entropy is a generalization of the Deng entropy and Shannon entropy. That is, the complex-valued Deng entropy can degenerate to classical Deng entropy when the complex-valued mass function degenerates to a mass function in real space. In addition, the proposed complex-valued Deng entropy can also degenerates to Shannon entropy when the complex-valued mass function degenerates to a probability distribution in real space. Some numerical examples demonstrate the compatibility and effectiveness of the complex-valued Deng entropy.

submitted time 2021-06-03 Hits6405Downloads545 Comment 0

2. chinaXiv:202106.00005 [pdf]

Complex-valued Renyi Entropy

Lipeng Pan; Yong Deng
Subjects: Computer Science >> Other Disciplines of Computer Science

Complex-valued expression models have been widely used in the application of intelligent decision systems. However, there is a lack of entropy to measure the uncertain information of the complex-valued probability distribution. Therefore, how to reasonably measure the uncertain information of the complex-valued probability distribution is a gap to be filled. In this paper, inspired by the Renyi entropy, we propose the Complex-valued Renyi entropy, which can measure uncertain information of the complex-valued probability distribution under the framework of complex numbers, and is also the first time to measure uncertain information in the complex space. The Complex-valued Renyi entropy contains the features of the classical Renyi entropy, i.e., the Complex-valued Renyi Entropy corresponds to different information functions with different parameters q. Meanwhile, the Complex-valued Renyi entropy has some properties, such as non-negativity, monotonicity, etc. Some numerical examples can demonstrate the flexibilities and reasonableness of the Complex-valued Renyi entropy.

submitted time 2021-05-31 Hits5645Downloads499 Comment 0

3. 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 Hits7210Downloads923 Comment 0

4. 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 Hits9999Downloads974 Comment 0

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