Special Issue "Recent Progress of Deng Entropy"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (31 December 2021).

Special Issue Editor

Dr. Yong Deng
E-Mail Website
Guest Editor
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
Interests: uncertainty measure; Shannon entropy; Tsallis entropy; Renyi entropy; Deng Entropy; evidence theory; fuzzy sets; fractal; complex network; time series

Special Issue Information

Dear Colleagues,

Uncertainty is ubiquitous in the natural world, which  covers an immense range of important phenomena in natural, life, and social sciences. In most cases, Shannon entropy can be used to measure the uncertainty, and has been used in many fields. However, Shannon entropy can often be hindered in systems in which some subsystems are not mutually exclusive, which means that uncertainty is far from being understood on a fundamental level. In many fields, an incremental understanding of underlying principles would mean significant progress. Deng proposed Deng entropy to measure the uncertainty in Dempster–Shafer evidence theory, which has been used in many fields.

Further progress on this front calls for a new method based on uncertainty measurement, as well as for an improved understanding of the meaning of entropy. The focus of this Special Issue is the theoretical development, as well as interesting applications of, uncertainty or entropy measurement by uncovering new phenomena or shedding new light on known events in different scientific fields. The latest studies on the topic focus on Deng Entropy (https://0-doi-org.brum.beds.ac.uk/10.1016/j.chaos.2016.07.014), Uncertainty Measurement in Evidence Theory (https://0-doi-org.brum.beds.ac.uk/10.1007/s11432-020-3006-9), and Information Volume of Mass Function (https://0-doi-org.brum.beds.ac.uk/10.15837/ijccc.2020.6.3983) , which can provide the readers with novel ideas and methods.

Dr. Yong Deng
Guest Editor

Manuscript Submission Information

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Keywords

  • Uncertainty
  • Entropy
  • Fuzzy Entropy
  • Belief Entropy
  • Deng Entropy
  • Information theory
  • Quantum theory
  • Dynamic system
  • Artificial intelligence
  • Decision-making

Published Papers (5 papers)

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Research

Article
Threat Assessment Method of Low Altitude Slow Small (LSS) Targets Based on Information Entropy and AHP
Entropy 2021, 23(10), 1292; https://0-doi-org.brum.beds.ac.uk/10.3390/e23101292 - 30 Sep 2021
Viewed by 374
Abstract
In order to deal with the new threat of low altitude slow small (LSS) targets in air defense operations and provide support for LSS target interception decision, we propose a simple and reliable LSS target threat assessment method. Based on the detection capability [...] Read more.
In order to deal with the new threat of low altitude slow small (LSS) targets in air defense operations and provide support for LSS target interception decision, we propose a simple and reliable LSS target threat assessment method. Based on the detection capability of LSS targets and their threat characteristics, this paper proposes a threat evaluation factor and threat degree quantization function in line with the characteristics of LSS targets. LSS targets not only have the same threat characteristics as traditional air targets but also have the unique characteristics of flexible mobility and dynamic mission planning. Therefore, we use analytic hierarchy process (AHP) and information entropy to determine the subjective and objective threat factor weights of LSS targets and use the optimization model to combine them to obtain more reliable evaluation weights. Finally, the effectiveness and credibility of the proposed method are verified by experimental simulation. Full article
(This article belongs to the Special Issue Recent Progress of Deng Entropy)
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Article
Uncertainty of Interval Type-2 Fuzzy Sets Based on Fuzzy Belief Entropy
Entropy 2021, 23(10), 1265; https://0-doi-org.brum.beds.ac.uk/10.3390/e23101265 - 28 Sep 2021
Viewed by 347
Abstract
Interval type-2 fuzzy sets (IT2 FS) play an important part in dealing with uncertain applications. However, how to measure the uncertainty of IT2 FS is still an open issue. The specific objective of this study is to present a new entropy named fuzzy [...] Read more.
Interval type-2 fuzzy sets (IT2 FS) play an important part in dealing with uncertain applications. However, how to measure the uncertainty of IT2 FS is still an open issue. The specific objective of this study is to present a new entropy named fuzzy belief entropy to solve the problem based on the relation among IT2 FS, belief structure, and Z-valuations. The interval of membership function can be transformed to interval BPA [Bel,Pl]. Then, Bel and Pl are put into the proposed entropy to calculate the uncertainty from the three aspects of fuzziness, discord, and nonspecificity, respectively, which makes the result more reasonable. Compared with other methods, fuzzy belief entropy is more reasonable because it can measure the uncertainty caused by multielement fuzzy subsets. Furthermore, when the membership function belongs to type-1 fuzzy sets, fuzzy belief entropy degenerates to Shannon entropy. Compared with other methods, several numerical examples are demonstrated that the proposed entropy is feasible and persuasive. Full article
(This article belongs to the Special Issue Recent Progress of Deng Entropy)
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Article
A Novel Conflict Management Method Based on Uncertainty of Evidence and Reinforcement Learning for Multi-Sensor Information Fusion
Entropy 2021, 23(9), 1222; https://0-doi-org.brum.beds.ac.uk/10.3390/e23091222 - 17 Sep 2021
Cited by 1 | Viewed by 524
Abstract
Dempster–Shafer theory (DST), which is widely used in information fusion, can process uncertain information without prior information; however, when the evidence to combine is highly conflicting, it may lead to counter-intuitive results. Moreover, the existing methods are not strong enough to process real-time [...] Read more.
Dempster–Shafer theory (DST), which is widely used in information fusion, can process uncertain information without prior information; however, when the evidence to combine is highly conflicting, it may lead to counter-intuitive results. Moreover, the existing methods are not strong enough to process real-time and online conflicting evidence. In order to solve the above problems, a novel information fusion method is proposed in this paper. The proposed method combines the uncertainty of evidence and reinforcement learning (RL). Specifically, we consider two uncertainty degrees: the uncertainty of the original basic probability assignment (BPA) and the uncertainty of its negation. Then, Deng entropy is used to measure the uncertainty of BPAs. Two uncertainty degrees are considered as the condition of measuring information quality. Then, the adaptive conflict processing is performed by RL and the combination two uncertainty degrees. The next step is to compute Dempster’s combination rule (DCR) to achieve multi-sensor information fusion. Finally, a decision scheme based on correlation coefficient is used to make the decision. The proposed method not only realizes adaptive conflict evidence management, but also improves the accuracy of multi-sensor information fusion and reduces information loss. Numerical examples verify the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Recent Progress of Deng Entropy)
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Article
Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making
Entropy 2021, 23(9), 1119; https://0-doi-org.brum.beds.ac.uk/10.3390/e23091119 - 28 Aug 2021
Cited by 1 | Viewed by 546
Abstract
Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov’s intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. [...] Read more.
Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov’s intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method. Full article
(This article belongs to the Special Issue Recent Progress of Deng Entropy)
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Article
A New Total Uncertainty Measure from A Perspective of Maximum Entropy Requirement
Entropy 2021, 23(8), 1061; https://0-doi-org.brum.beds.ac.uk/10.3390/e23081061 - 17 Aug 2021
Viewed by 446
Abstract
The Dempster-Shafer theory (DST) is an information fusion framework and widely used in many fields. However, the uncertainty measure of a basic probability assignment (BPA) is still an open issue in DST. There are many methods to quantify the uncertainty of BPAs. However, [...] Read more.
The Dempster-Shafer theory (DST) is an information fusion framework and widely used in many fields. However, the uncertainty measure of a basic probability assignment (BPA) is still an open issue in DST. There are many methods to quantify the uncertainty of BPAs. However, the existing methods have some limitations. In this paper, a new total uncertainty measure from a perspective of maximum entropy requirement is proposed. The proposed method can measure both dissonance and non-specificity in BPA, which includes two components. The first component is consistent with Yager’s dissonance measure. The second component is the non-specificity measurement with different functions. We also prove the desirable properties of the proposed method. Besides, numerical examples and applications are provided to illustrate the effectiveness of the proposed total uncertainty measure. Full article
(This article belongs to the Special Issue Recent Progress of Deng Entropy)
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