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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 Hits6424Downloads555 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 Hits5656Downloads505 Comment 0

3. chinaXiv:202104.00004 [pdf]

QZNs: Quantum Z-numbers

Deng, Jixiang; Deng, Yong
Subjects: Computer Science >> Integration Theory of Computer Science

Because of the efficiency of modeling fuzziness and vagueness, Z-number plays an important role in real practice. However, Z-numbers, defined in the real number field, lack the ability to process the quantum information in quantum environment. It is reasonable to generalize Z-number into its quantum counterpart. In this paper, we propose quantum Z-numbers (QZNs), which are the quantum generalization of Z-numbers. In addition, seven basic quantum fuzzy operations of QZNs and their corresponding quantum circuits are presented and illustrated by numerical examples. Moreover, based on QZNs, a novel quantum multi-attributes decision making (MADM) algorithm is proposed and applied in medical diagnosis. The results show that, with the help of quantum computation, the proposed algorithm can make diagnoses correctly and efficiently.

submitted time 2021-04-12 Hits5940Downloads646 Comment 0

4. 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 Hits7237Downloads940 Comment 0

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