1
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Zhou J, Li Z, Deng Y. Random walk in random permutation set theory. CHAOS (WOODBURY, N.Y.) 2024; 34:093137. [PMID: 39321470 DOI: 10.1063/5.0220154] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2024] [Accepted: 09/03/2024] [Indexed: 09/27/2024]
Abstract
Random walk is an explainable approach for modeling natural processes at the molecular level. The random permutation set theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer theory. Recent explorations indicate a promising link between RPST and random walk. In this study, we conduct an analysis and construct a random walk model based on the properties of RPST, with Monte Carlo simulations of such random walk. Our findings reveal that the random walk generated through RPST exhibits characteristics similar to those of a Gaussian random walk and can be transformed into a Wiener process through a specific limiting scaling procedure. This investigation establishes a novel connection between RPST and random walk theory, thereby not only expanding the applicability of RPST but also demonstrating the potential for combining the strengths of both approaches to improve problem-solving abilities.
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Affiliation(s)
- Jiefeng Zhou
- Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Zhen Li
- China Mobile Information Technology Center, Beijing 100029, China
| | - Yong Deng
- Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 610054, China
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2
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Su X, Shang S, Xiong L, Hong Z, Zhong J. Research on dependent evidence combination based on principal component analysis. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:4853-4873. [PMID: 38872517 DOI: 10.3934/mbe.2024214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2024]
Abstract
Dempster-Shafer evidence theory, as a generalization of probability theory, is a powerful tool for dealing with a variety of uncertainties, such as incompleteness, ambiguity, and conflict. Because of its advantages in information fusion compared with traditional probability theory, it is widely used in various fields. However, the classic Dempster's combination rule assumes that evidences are independent of each other, which is difficult to satisfy in real life. Ignoring the dependence among the evidences will lead to unreasonable fusion results, and even wrong conclusions. Considering the limitations of D-S evidence theory, this paper proposed a new evidence fusion model based on principal component analysis (PCA) to deal with the dependence among evidences. First, the approximate independent principal components of each information source were obtained based on principal component analysis. Second, the principal component data set was used as a new information source for evidence theory. Third, the basic belief assignments (BBAs) were constructed. As the fundamental construct of evidence theory, a BBA is a probabilistic function corresponding to each hypothesis, quantifying the belief assigned based on the evidence at hand. This function facilitates the synthesis of disparate evidence sources into a mathematically coherent and unified belief structure. After constructing the BBAs, the BBAs were fused and a conclusion was drawn. The case study verified that the proposed method is more robust than several traditional methods and can deal with redundant information effectively to obtain more stable results.
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Affiliation(s)
- Xiaoyan Su
- School of Automation Engineering, Shanghai University of Electric Power, Shanghai 200090, China
| | - Shuwen Shang
- School of Automation Engineering, Shanghai University of Electric Power, Shanghai 200090, China
| | - Leihui Xiong
- State Grid Nanchang Electric Power Supply Company, Nanchang 330069, China
| | - Ziying Hong
- School of Automation Engineering, Shanghai University of Electric Power, Shanghai 200090, China
| | - Jian Zhong
- School of Automation Engineering, Shanghai University of Electric Power, Shanghai 200090, China
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3
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Huang Y, Xiao F, Cao Z, Lin CT. Higher Order Fractal Belief Rényi Divergence With Its Applications in Pattern Classification. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2023; 45:14709-14726. [PMID: 37651495 DOI: 10.1109/tpami.2023.3310594] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
Information can be quantified and expressed by uncertainty, and improving the decision level of uncertain information is vital in modeling and processing uncertain information. Dempster-Shafer evidence theory can model and process uncertain information effectively. However, the Dempster combination rule may provide counter-intuitive results when dealing with highly conflicting information, leading to a decline in decision level. Thus, measuring conflict is significant in the improvement of decision level. Motivated by this issue, this paper proposes a novel method to measure the discrepancy between bodies of evidence. First, the model of dynamic fractal probability transformation is proposed to effectively obtain more information about the non-specificity of basic belief assignments (BBAs). Then, we propose the higher-order fractal belief Rényi divergence (HOFBReD). HOFBReD can effectively measure the discrepancy between BBAs. Moreover, it is the first belief Rényi divergence that can measure the discrepancy between BBAs with dynamic fractal probability transformation. HoFBReD has several properties in terms of probability transformation as well as measurement. When the dynamic fractal probability transformation ends, HoFBReD is equivalent to measuring the Rényi divergence between the pignistic probability transformations of BBAs. When the BBAs degenerate to the probability distributions, HoFBReD will also degenerate to or be related to several well-known divergences. In addition, based on HoFBReD, a novel multisource information fusion algorithm is proposed. A pattern classification experiment with real-world datasets is presented to compare the proposed algorithm with other methods. The experiment results indicate that the proposed algorithm has a higher average pattern recognition accuracy with all datasets than other methods. The proposed discrepancy measurement method and multisource information algorithm contribute to the improvement of decision level.
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Zhou C, Xu D, Wang Z. Conversion and fusion method of multi-source and different populations maintainability prior data. Heliyon 2023; 9:e21208. [PMID: 37954291 PMCID: PMC10632692 DOI: 10.1016/j.heliyon.2023.e21208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Revised: 08/27/2023] [Accepted: 10/18/2023] [Indexed: 11/14/2023] Open
Abstract
Maintainability is an important universal quality characteristic that reflects the convenience, speed and economy of weapon and equipment maintenance. Making full use of multi-source data to accurately verify the degree to which the developed equipment meets the maintainability requirements is an important basis for equipment identification and acceptance. To solve the low reliability of equipment maintainability verification results caused by inaccurate comprehensive prior distribution obtained by fusing multi-source and different populations' prior data, a method of data conversion and fusion is proposed. A data conversion model based on the mean value ratio of failure mode maintenance data is constructed. The conversion factor is defined according to objective data to convert the different populations' prior data to the same populations. Next, a comparison of the prior distribution fitting performance of Bayes bootstrap, bootstrap, and two improved sample-resampling methods to are used obtain the closest fitting distribution to the true distribution. By constructing a multi-source data fusion model based on improved KL divergence, a symmetrical KL divergence is constructed to describe the similarity between each prior distribution and the field distribution for the weighted fusion of multi-source prior distribution in addition to determining and testing the normal comprehensive prior distribution. The results show that the conversion and fusion method effectively converts the multi-source and different populations' maintainability prior data and obtains an accurate, comprehensive prior distribution by fusion, laying the foundation for applying the Bayes test method to verify the quantitative index of equipment maintainability.
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Affiliation(s)
- Cheng Zhou
- Department of Arms and Control, Army Academy of Armored Forces, Beijing, 100072, China
| | - Da Xu
- Department of Arms and Control, Army Academy of Armored Forces, Beijing, 100072, China
| | - Zhaoyang Wang
- Department of Arms and Control, Army Academy of Armored Forces, Beijing, 100072, China
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5
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Zhang Z, Wang H, Zhang J, Jiang W. A New Correlation Measure for Belief Functions and Their Application in Data Fusion. ENTROPY (BASEL, SWITZERLAND) 2023; 25:925. [PMID: 37372269 PMCID: PMC10297068 DOI: 10.3390/e25060925] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Revised: 06/07/2023] [Accepted: 06/08/2023] [Indexed: 06/29/2023]
Abstract
Measuring the correlation between belief functions is an important issue in Dempster-Shafer theory. From the perspective of uncertainty, analyzing the correlation may provide a more comprehensive reference for uncertain information processing. However, existing studies about correlation have not combined it with uncertainty. In order to address the problem, this paper proposes a new correlation measure based on belief entropy and relative entropy, named a belief correlation measure. This measure takes into account the influence of information uncertainty on their relevance, which can provide a more comprehensive measure for quantifying the correlation between belief functions. Meanwhile, the belief correlation measure has the mathematical properties of probabilistic consistency, non-negativity, non-degeneracy, boundedness, orthogonality, and symmetry. Furthermore, based on the belief correlation measure, an information fusion method is proposed. It introduces the objective weight and subjective weight to assess the credibility and usability of belief functions, thus providing a more comprehensive measurement for each piece of evidence. Numerical examples and application cases in multi-source data fusion demonstrate that the proposed method is effective.
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Affiliation(s)
- Zhuo Zhang
- School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, China; (Z.Z.); (H.W.)
| | - Hongfei Wang
- School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, China; (Z.Z.); (H.W.)
| | - Jianting Zhang
- No. 91977 Unit of People’s Liberation Army of China, Beijing 100036, China;
| | - Wen Jiang
- School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, China; (Z.Z.); (H.W.)
- National Engineering Laboratory for Integrated Aero-Space-Ground-Ocean Big Data Application Technology, Xi’an 710072, China
- Peng Cheng Laboratory, Shenzhen 518055, China
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6
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Qiang C, Li Z, Deng Y. Multifractal analysis of mass function. Soft comput 2023; 27:1-14. [PMID: 37362275 PMCID: PMC10233544 DOI: 10.1007/s00500-023-08502-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 05/02/2023] [Indexed: 06/28/2023]
Abstract
In order to explore the fractal characteristic in Dempster-Shafer evidence theory, a fractal dimension of mass function is proposed recently, to reveal the invariance of scale of belief entropy. When mass function degenerates to probability, the fractal dimension is equivalent to classical Renyi information dimension only with α = 1 , which can measure the change rate of Shannon entropy with the size of framework. For Renyi dimension, different parameters α represent the relationship between different entropies and framework size. However, this compatibility is not shown in existing fractal dimension. Thus, in this paper, we introduce parameter α to generalize the existing dimension. Due to the diversity of the value of α , we name the new dimension: multifractal dimension of mass function. In addition, inspired by multifractal spectrum of Cantor set, we explore the relation between the belief degree of focal element and the number of focal element with same belief degree for some special assignments. Relevant results are also presented by spectrum. We provide a static discounting coefficient generating method to modify mass function to improve the accuracy of classify result. The experiment is conducted in three datasets, and the result shows the effectiveness of our method.
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Affiliation(s)
- Chenhui Qiang
- Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 610054 China
- Yingcai Honors College, University of Electronic Science and Technology of China, Chengdu, 610054 China
| | - Zhen Li
- China Mobile Information Technology Center, Beijing, 100029 China
| | - Yong Deng
- School of Medicine, Vanderbilt University, Nashville, TN 37240 USA
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7
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Shi J, Wang W, Lou X, Zhang S, Li X. Parameterized Hamiltonian Learning With Quantum Circuit. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2023; 45:6086-6095. [PMID: 36044483 DOI: 10.1109/tpami.2022.3203157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Hamiltonian learning, as an important quantum machine learning technique, provides a significant approach for determining an accurate quantum system. This paper establishes parameterized Hamiltonian learning (PHL) and explores its application and implementation on quantum computers. A parameterized quantum circuit for Hamiltonian learning is first created by decomposing unitary operators to excite the system evolution. Then, a PHL algorithm is developed to prepare a specific Hamiltonian system by iteratively updating the gradient of the loss function about circuit parameters. Finally, the experiments are conducted on Origin Pilot, and it demonstrates that the PHL algorithm can deal with the image segmentation problem and provide a segmentation solution accurately. Compared with the classical Grabcut algorithm, the PHL algorithm eliminates the requirement of early manual intervention. It provides a new possibility for solving practical application problems with quantum devices, which also assists in solving increasingly complicated problems and supports a much wider range of application possibilities in the future.
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8
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KNN Data Filling Algorithm for Incomplete Interval-Valued Fuzzy Soft Sets. INT J COMPUT INT SYS 2023. [DOI: 10.1007/s44196-023-00190-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/13/2023] Open
Abstract
AbstractAs a generalization of the fuzzy soft set, interval-valued fuzzy soft set is viewed as a more resilient and powerful tool for dealing with uncertain information. However, the lower or upper membership degree, or both of them, may be missed during the data collection and transmission procedure, which could present challenges for data processing. The existing data filling algorithm for the incomplete interval-valued fuzzy soft sets has low accuracy and the high error rate which leads to wrong filling results and involves subjectivity due to setting the threshold. Therefore, to solve these problems, we propose a KNN data filling algorithm for the incomplete interval-valued fuzzy soft sets. An attribute-based combining rule is first designed to determine whether the data involving incomplete membership degree should be ignored or filled which avoids subjectivity. The incomplete data will be filled according to their K complete nearest neighbors. To verify the validity and feasibility of the method, we conduct the randomized experiments on the real dataset as Shanghai Five-Four Hotel Data set and simulated datasets. The experimental results illustrate that our proposed method outperform the existing method on the average accuracy rate and error rate.
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9
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Ordinal belief entropy. Soft comput 2023. [DOI: 10.1007/s00500-023-07947-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/09/2023]
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10
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Huang Y, Xiao F. Higher Order Belief Divergence with Its Application in Pattern Classification. Inf Sci (N Y) 2023. [DOI: 10.1016/j.ins.2023.03.095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
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11
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Chen L, Deng Y. Entropy of Random Permutation Set. COMMUN STAT-THEOR M 2023. [DOI: 10.1080/03610926.2023.2173975] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/23/2023]
Affiliation(s)
- Luyuan Chen
- Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, China
| | - Yong Deng
- Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, China
- School of Medicine, Vanderbilt University, Nashville, Tennessee, China
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12
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Li S, Xiao F. A mechanics model based on information entropy for identifying influencers in complex networks. APPL INTELL 2023; 53:1-20. [PMID: 36741743 PMCID: PMC9885924 DOI: 10.1007/s10489-023-04457-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 01/05/2023] [Indexed: 01/31/2023]
Abstract
The network, with some or all characteristics of scale-free, self-similarity, self-organization, attractor and small world, is defined as a complex network. The identification of significant spreaders is an indispensable research direction in complex networks, which aims to discover nodes that play a crucial role in the structure and function of the network. Since influencers are essential for studying the security of the network and controlling the propagation process of the network, their assessment methods are of great significance and practical value to solve many problems. However, how to effectively combine global information with local information is still an open problem. To solve this problem, the generalized mechanics model is further improved in this paper. A generalized mechanics model based on information entropy is proposed to discover crucial spreaders in complex networks. The influence of each neighbor node on local information is quantified by information entropy, and the interaction between each node on global information is considered by calculating the shortest distance. Extensive tests on eleven real networks indicate the proposed approach is much faster and more precise than traditional ways and state-of-the-art benchmarks. At the same time, it is effective to use our approach to identify influencers in complex networks.
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Affiliation(s)
- Shuyu Li
- Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University, Shanghai, 200092 China
- School of Big Data and Software Engineering, Chongqing University, Chongqing, 401331 China
| | - Fuyuan Xiao
- School of Big Data and Software Engineering, Chongqing University, Chongqing, 401331 China
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13
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Wang Z, Zhou Q, Deng Y. Belief entropy rate: a method to measure the uncertainty of interval-valued stochastic processes. APPL INTELL 2023. [DOI: 10.1007/s10489-022-04407-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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14
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Chen L, Deng Y, Cheong KH. The distance of Random Permutation Set. Inf Sci (N Y) 2023. [DOI: 10.1016/j.ins.2023.01.105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
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15
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Chen Z, Zhou J, Sun R. A multi-source heterogeneous spatial big data fusion method based on multiple similarity and voting decision. Soft comput 2022. [DOI: 10.1007/s00500-022-07734-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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16
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Liu J, Xiao F. Gini eXtropy. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2154798] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Jiali Liu
- School of Computer and Information Science, Southwest University, Chongqing, China
| | - Fuyuan Xiao
- School of Big Data and Software Engineering, Chongqing University, Chongqing, China
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17
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An Exponential Negation of Complex Basic Belief Assignment in Complex Evidence Theory. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.11.160] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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18
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Determine the number of unknown targets in the open world from the perspective of bidirectional analysis using Gap statistic and Isolation forest. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.12.034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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19
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Li J, Zhao A, Liu H. A Decision Probability Transformation Method Based on the Neural Network. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1638. [PMID: 36421493 PMCID: PMC9689871 DOI: 10.3390/e24111638] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Revised: 10/31/2022] [Accepted: 11/08/2022] [Indexed: 06/16/2023]
Abstract
When the Dempster-Shafer evidence theory is applied to the field of information fusion, how to reasonably transform the basic probability assignment (BPA) into probability to improve decision-making efficiency has been a key challenge. To address this challenge, this paper proposes an efficient probability transformation method based on neural network to achieve the transformation from the BPA to the probabilistic decision. First, a neural network is constructed based on the BPA of propositions in the mass function. Next, the average information content and the interval information content are used to quantify the information contained in each proposition subset and combined to construct the weighting function with parameter r. Then, the BPA of the input layer and the bias units are allocated to the proposition subset in each hidden layer according to the weight factors until the probability of each single-element proposition with the variable is output. Finally, the parameter r and the optimal transform results are obtained under the premise of maximizing the probabilistic information content. The proposed method satisfies the consistency of the upper and lower boundaries of each proposition. Extensive examples and a practical application show that, compared with the other methods, the proposed method not only has higher applicability, but also has lower uncertainty regarding the transformation result information.
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20
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A TFN-based Uncertainty Modeling Method in Complex Evidence Theory for Decision Making. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.11.014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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21
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Visualization of basic probability assignment. Soft comput 2022. [DOI: 10.1007/s00500-022-07412-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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22
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Zheng L, Xiao F. Complex interval number‐based uncertainty modeling method with its application in decision fusion. INT J INTELL SYST 2022. [DOI: 10.1002/int.23070] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Lingtao Zheng
- School of Big Data and Software Engineering Chongqing University Chongqing China
| | - Fuyuan Xiao
- School of Big Data and Software Engineering Chongqing University Chongqing China
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23
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Pan L, Gao X, Deng Y. Quantum algorithm of Dempster rule of combination. APPL INTELL 2022. [DOI: 10.1007/s10489-022-03877-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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24
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Gao B, Zhou Q, Deng Y. BIM-AFA: Belief information measure-based attribute fusion approach in improving the quality of uncertain data. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.07.026] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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25
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Zhu C, Xiao F, Cao Z. A generalized Rényi divergence for multi-source information fusion with its application in EEG data analysis. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.05.012] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
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26
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Wang Z, Xiao F, Cao Z. Uncertainty measurements for Pythagorean fuzzy set and their applications in multiple-criteria decision making. Soft comput 2022. [DOI: 10.1007/s00500-022-07361-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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27
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Identify influential nodes in network of networks from the view of weighted information fusion. APPL INTELL 2022. [DOI: 10.1007/s10489-022-03856-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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28
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