Combination of Evidential Sensor Reports with Distance Function and Belief Entropy in Fault Diagnosis

Yukun Dong, Jiantao Zhang, Zhen Li, Yong Hu, Yong Deng


Although evidence theory has been applied in sensor data fusion, it will have unreasonable results when handling highly conflicting sensor reports. To address the issue, an improved fusing method with evidence distance and belief entropy is proposed. Generally, the goal is to obtain the appropriate weights assigning to different reports. Specifically, the distribution difference between two sensor reports is measured by belief entropy. The diversity degree is presented by the combination of evidence distance and the distribution difference. Then, the weight of each sensor report is determined based on the proposed diversity degree. Finally, we can use Dempster combination rule to make the decision. A real application in fault diagnosis and an example show the efficiency of the proposed method. Compared with the existing methods, the method not only has a better performance of convergence, but also less uncertainty.


Dempster-Shafer evidence theory, sensor data fusion, fault diagnosis, evidence distance, belief entropy, information volume

Full Text:



Abellan, J. (2017). Analyzing properties of Deng entropy in the theory of evidence, Chaos Solitons & Fractals, 95, 195-199, 2017.

An, J.Y.; Hu, M.; Fu, L.; Zhan, J.W. (2019). A novel fuzzy approach for combining uncertain conflict evidences in the Dempster-Shafer theory, IEEE Access, 7, 7481-7501, 2019.

Cui, H.; Liu, Q.; Zhang, J.; Kang, B. (2019). An improved Deng entropy and its application in pattern recognition, IEEE Access, 7,18284-18292, 2019.

Dempster, A.P. (1967). Upper and lower probabilities induced by a multivalued mapping, Annals of Mathematics and Statistics, 38(2), 325-339, 1967.

Deng, Y.; Shi, W.K.; Zhu, Z.F.; Liu, Q. (2004). Combining belief functions based on distance of evidence, Decision Support Systems, 38(3), 489-493, 2004.

Deng, Y. (2106). Deng entropy, Chaos, Solitons & Fractals, 91, 549-553, 2016.

Deng, W.; Deng, Y. (2018). Entropic methodology for entanglement measures, Physica A: Statistical Mechanics and its Applications, 512, 693-697, 2018.

Deng, X.Y.; Deng, Y. (2019). D-AHP method with different credibility of information, Soft Computing, 23(2), 683-691, 2019.

Deng, X.Y.; Jiang, W. (2019). D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment, International Journal of Approximate Reasoning, 106, 194-213, 2019.

Deng, X.Y.; Jiang, W.; Wang, Z. (2019). Zero-sum polymatrix games with link uncertainty: A Dempster-Shafer theory solution, Applied Mathematics and Computation, 340, 101-112, 2019.

Dong, Y.K.; Wang, J.Y.; Chen, F.H.; Hu, Y.; Deng, Y. (2017). Location of Facility Based on Simulated Annealing and "ZKW" Algorithms, Mathematical Problems in Engineering, 2017, 9, 2017.

Dubois, D.; Prade, H. (1988). Representation and combination of uncertainty with belief functions and possibility measures, Computational Intelligence, 4(3), 244-264, 1988.

Dutta, P. (2017). Modeling of variability and uncertainty in human health risk assessment, MethodsX, 4, 76-85, 2017.

Dutta, P. (2018). An uncertainty measure and fusion rule for conflict evidences of big data via Dempster-Shafer theory, International Journal of Image and Data Fusion, 9(2), 152-169, 2018.

Dzitac, I.; Filip, F.G.; Manolescu, M.J. (2017). Fuzzy logic is not fuzzy: World-renowned computer scientist Lotfi A. Zadeh, International Journal of Computers Communications & Control, 12(6), 748-789, 2017.

Fan, X.F.; Zuo, M.J. (2006). Fault diagnosis of machines based on D-S evidence theory. Part 1: D-S evidence theory and its improvement, Pattern Recognition Letters, 27(5), 366-376, 2006.

Fei, L.G.; Deng, Y. (2019). A new divergence measure for basic probability assignment and its applications in extremely uncertain environments, International Journal of Intelligent Systems, 34(4), 584-600, 2019.

Fei, L.; Deng, Y. (2018). Identifying influential nodes in complex networks based on the inverse-square law, Physica A: Statistical Mechanics and its Applications, 512, 1044-1059, 2018.

Gao, X.; Deng, Y. (2019). The negation of basic probability assignment, IEEE Access, 7, 10.1109/ACCESS.2019.2901932, 2019.

Haenni, R. (2002). Are alternatives to Dempster's rule of combination real alternatives?: Comments on: About the belief function combination and the conflict management problem--Lefevre et al, Information Fusion, 3(3), 237-239, 2002.

Han, Y.; Deng, Y. (2019). A novel matrix game with payoffs of Maxitive Belief Structure, International Journal of Intelligent Systems, 34(4), 690-706, 2019.

Han, Y.; Deng, Y. (2018). A hybrid intelligent model for Assessment of critical success factors in high risk emergency system, Journal of Ambient Intelligence and Humanized Computing, 9(6), 1933-1953, 2018.

Han, Y.; Deng, Y. (2018). An Evidential Fractal AHP target recognition method, Defence Science Journal, 68(4), 367-373, 2018.

Jaunzemis, A.D.; Holzinger, M.J.; Chan, M.W.; Shenoy, P.P. (2019). Evidence gathering for hypothesis resolution using judicial evidential reasoning, Information Fusion, 49, 26-45, 2019.

Jiang, W.; Wei, B.Y.; Xie, C.H.; Zhou, D.Y. (2016). An evidential sensor fusion method in fault diagnosis, Advances in Mechanical Engineering, 8(3), 1-7, 2016.

Jiang, W. (2018). A correlation coefficient for belief functions, International Journal of Approximate Reasoning, 103, 94-106, 2018.

Jiang, W.; Wang, S.Y. (2017). An Uncertainty Measure for Interval-valued Evidences, International Journal of Computers Communications & Control, 12(5), 631-644, 2017.

Jin, L.Q.; Fang, X. (2017). Interval Certitude Rule Base Inference Method using the Evidential Reasoning, International Journal of Computers Communications & Control, 12(6), 2017.

Jousselme, A.L.; Grenier, D.; Bossé, É, (2001). A new distance between two bodies of evidence, Information Fusion, 2(2), 91-101, 2001.

Kang, B.Y.; Zhang, P.D.; Gao, Z.Y.; Chhipi-Shrestha, G.; Hewage, K.; Sadiq, R. (2019). Environmental assessment under uncertainty using Dempster-Shafer theory and Z-numbers, Journal of Ambient Intelligence and Humanized Computing,, 2019.

Kang, B.Y.; Deng, Y.; Hewage, K.; Sadiq, R. (2019). A method of measuring uncertainty for Z-number, IEEE Transactions on Fuzzy Systems, 27(4), 731-738, 2019.

Kuzemsky, A.L. (2018). Temporal evolution, directionality of time and irreversibility, Rivista Del Nuovo Cimento, 41(10), 513-574, 2018.

Lefevre, E.; Colot, O.; Vannoorenberghe, P. (2002). Belief function combination and conflict management, Information fusion, 3(2), 149-162, 2002.

Li, M.Z.; Zhang, Q.; Deng, Y. (2018). Evidential identification of influential nodes in network of networks, Chaos, Solitons & Fractals, 117, 283-296, 2018.

Li, Y.X.; Deng, Y. (2018). Generalized Ordered Propositions Fusion Based on Belief Entropy, International Journal of Computers Communications & Control, 13(5), 792-807, 2018.

Liu, C.;Li, L.; Wang, Z.; Wang, R.(2019). Pattern transitions in a vegetation system with cross-diffusion, Applied Mathematics and Computation, 342, 255-262, 2019.

Liu, H.; Dzitac, I.; Guo, S.(2018). Reduction of Conditional Factors in Causal Analysis, International Journal of Computers Communications & Control, 13(3), 383-390, 2018.

Meng, D.; Yang, S.; Zhang, Y.; Zhu, S (2018). Structural reliability analysis and uncertainties-based collaborative design and optimization of turbine blades using surrogate model, Fatigue & Fracture of Engineering Materials & Structures, 10.1111/ffe.12906, 2018.

Meng, D.; Liu, M.; Yang, S.; Zhang, H.; Ding, R. (2018). A fluid-structure analysis approach and its application in the uncertainty-based multidisciplinary design and optimization for blades, Advances in Mechanical Engineering, 10(6), 1687814018783410, 2018.

Meng, D.; Li, Y.; Zhu, S.; Lv, G.; Correia, J.; de Jesus, A.(2019). An Enhanced Reliability Index Method and Its Application in Reliability-Based Collaborative Design and Optimization, Mathematical Problems in Engineering,, 2019.

Mo, H.M.; Deng, Y. (2019). An evaluation for sustainable mobility extended by D numbers, Technological and Economic Development of Economy, Accepted, 2019.

Murphy, C.K. (2000); Combining belief functions when evidence conflicts, Decision Support Systems, 29(1), 1-9, 2000.

Pan, L.P.; Deng, Y. (2018). A New Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Belief Function and Plausibility Function, Entropy, 20(11), 842, 2018.

Paté-Cornell, M.E. (1990). Organizational Aspects of Engineering System, Safety Science, 250, 1210-16, 1990.

Rong, H.; Ge, M.; Zhang, G.; Zhu, M. (2018). An approach for detecting fault lines in a small current grounding system using fuzzy reasoning spiking neural p systems, International Journal of Computers Communications & Control, 13(4), 521-536, 2018.

Sabahi, F. (2016). A Novel Generalized Belief Structure Comprising Unprecisiated Uncertainty Applied to Aphasia Diagnosis, Journal of Biomedical Informatics, 62, 66-77, 2016.

Seiti, H.; Hafezalkotob, A. (2019). Developing the R-TOPSIS methodology for risk-based preventive maintenance planning: A case study in rolling mill company, Computers & Industrial Engineering, 128, 622-636, 2019.

Seiti, H.; Hafezalkotob, A.; Martinez, L. (2019). R-numbers, a new risk modeling associated with fuzzy numbers and its application to decision making, Information Sciences, 483, 206- 231, 2019.

Shafer, G. (1967). A Mathematical Theory of Evidence, Princeton University Press, 1967.

Smets, P. (1993). Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem, International Journal of Approximate Reasoning, 9(1), 1-35, 1993.

Smets, P.; Kennes, R. (1994). The transferable belief model, Artificial Intelligence, 66(2), 191-234, 1994.

Song, Y.T.; Deng, Y. (2019). A new method to measure the divergence in evidential sensor data fusion, International Journal of Distributed Sensor Networks, 15(4), DOI: 10.1177/1550147719841295, 2019.

Su, X.Y.; Li, L.S.; Shi, F.J.; Qian, H. (2018). Research on the Fusion of Dependent Evidence Based on Mutual Information, IEEE Access, 6, 71839-71845, 2018.

Su, X.Y.; Li, L.S.; Qian, H.; Sankaran, M.; Deng, Y. (2019). A new rule to combine dependent bodies of evidence, Soft Computing,, 2019.

Sun, R.L.; Deng, Y. (2019); A new method to identify incomplete frame of discernment in evidence theory, IEEE Access, 7(1), 15547-15555, 2019.

Sun, R.L.; Deng, Y. (2019). A new method to determine generalized basic probability assignment in the open world, IEEE Access, 7(1), accepted, 2019.

Vandoni, J.; Aldea, E.; Le Hégarat-Mascle, S. (2019). Evidential query-by-committee active learning for pedestrian detection in high-density crowds, International Journal of Approximate Reasoning, 104, 166-184, 2019.

Wang, T.; Zhang, G.X.; Rong, H.N.; Pérez-Jiménez, M.J. (2014). Application of fuzzy reasoning spiking neural P systems to fault diagnosis, International Journal of Computers Communications & Control, 9(6), 786-799, 2014.

Wang, Y.; Wang, S.; Deng, Y. (2019). A modified efficiency centrality to identify influential nodes in weighted networks, Pramana, 68(4), 68, 2019.

Wang, Y.J.; Deng, Y. (2018). Base belief function: an efficient method of conflict management, Journal of Ambient Intelligence and Humanized Computing,, 2018.

Wang, J.; Qiao, K.Y.; Zhang, Z.Y. (2019). An improvement for combination rule in evidence theory, Future Generation Computer Systems, 91, 1-9, 2019.

Wei, B.; Deng, Y. (2018). A cluster-growing dimension of complex networks: From the view of node closeness centrality, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2019.01.125, 2019.

Xiao, F.Y. (2018). A Hybrid Fuzzy Soft Sets Decision Making Method in Medical Diagnosis, IEEE Access, 6, 25300-25312, 2018.

Xiao, F.Y. (2018); A novel multi-criteria decision making method for assessing health-care waste treatment technologies based on D numbers, Engineering Applications of Artificial Intelligence, 71(2018), 216-225, 2018.

Xiao, F.Y. (2019). A multiple criteria decision-making method based on D numbers and belief entropy, International Journal of Fuzzy Systems, 00620-2, 2019.

Xiao, F.Y.; Ding, W.P. (2019). A novel multi-criteria decision making method for assessing health-care waste treatment technologies based on D numbers, Applied Soft Computing, 74, DOI: 10.1016/j.asoc.2019.03.043, 2019.

Xu, X.B.; Li, S.B.; Song, X.J.; Wen, C.L.; Xu, D.L. (2016). The optimal design of industrial alarm systems based on evidence theory, Control Engineering Practice, 46, 142-156, 2016.

Xu, H.; Deng, Y. (2019). Dependent Evidence Combination Based on DEMATEL Method, International Journal of Intelligent Systems, 34, 10.1002/int.22107, 2019.

Xu, P.; Zhang, R.; Deng, Y. (2019). A Novel Visibility Graph Transformation of Time Series into Weighted Networks, Chaos, Solitons & Fractals, 2018, 201-208, 2018.

Yager, R.R. (1987). On the Dempster-Shafer framework and new combination rules, Information Sciences, 41(2), 93-137, 1987.

Yang, H.C.; Deng, Y.; Jones, J. (2018). Network Division Method Based on Cellular Growth and Physarum-inspired Network Adaptation, International Journal of Unconventional Computing, 13(6), 477-491, 2018.

Yin, L.K.; Deng, Y. (2018). Toward uncertainty of weighted networks: An entropy-based model, Physica A: Statistical Mechanics and its Applications, 508, 176-186, 2018.

Yin, L.K.; Deng, X.Y.; Deng, Y. (2019). The negation of a basic probability assignment, IEEE Transactions on Fuzzy Systems, 27(1), 135-143, 2019.

Zadeh, L.A. (1965). Fuzzy Sets, Information and Control, 8(3), 338-353, 1965.

Zadeh, L.A. (1986). A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination, AI magazine, 7(2), 85, 1986.

Zavadskas, E.K.; Antucheviciene, J.; Hajiagha, S.H.R. (2015). The interval-valued intuitionistic fuzzy MULTIMOORA method for group decision making in engineering, Mathematical Problems in Engineering, 2015, 13, 2015.

Zavadskas, E.K.; Antucheviciene, J.; Turskis, Z.; Adeli, H. (2016). Hybrid multiple-criteria decision-making methods: A review of applications in engineering, Scientia Iranica. Transaction A, Civil Engineering, 23(1), 1, 2016.

Zhang, L.M.; Wu, X.G.; Qin, Y.W.; Skibniewski, M.J.; Liu, W.L. (2016). Towards a Fuzzy Bayesian Network Based Approach for Safety Risk Analysis of Tunnel-Induced Pipeline Damage, Risk Analysis, 36(2), 278-301, 2016.

Zhang, L.M.; Wu, X.G.; Zhu, H.P.; AbouRizk, S.M. (2017). Perceiving safety risk of buildings adjacent to tunneling excavation: An information fusion approach, Automation in Construction, 73, 88-101, 2017.

Zhang, W.Q.; Deng, Y. (2018). Combining conflicting evidence using the DEMATEL method, Soft computing,, 2018.

Zhang, H.P.; Deng, Y. (2018). Engine fault diagnosis based on sensor data fusion considering information quality and evidence theory, Advances in Mechanical Engineering, 10(11), DOI: 10.1177/1687814018809184, 2018.

Zhao, D.; Wang, L.; Wang, Z.; Xiao, G. (2019). Virus Propagation and Patch Distribution in Multiplex Networks: Modeling, Analysis, and Optimal Allocation, IEEE Transactions on Information Forensics and Security, 14(7), 1755-1767, 2019.

Zhu, W.B.; Yang, H.C.; Jin, Y.; Liu, B.Y. (2017). A Method for Recognizing Fatigue Driving Based on Dempster-Shafer Theory and Fuzzy Neural Network, Mathematical Problems in Engineering, 10, 2017.


Copyright (c) 2019 Yukun Dong, Jiantao Zhang, Zhen Li, Yong Hu, Yong Deng

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC-BY-NC  License for Website User

Articles published in IJCCC user license are protected by copyright.

Users can access, download, copy, translate the IJCCC articles for non-commercial purposes provided that users, but cannot redistribute, display or adapt:

  • Cite the article using an appropriate bibliographic citation: author(s), article title, journal, volume, issue, page numbers, year of publication, DOI, and the link to the definitive published version on IJCCC website;
  • Maintain the integrity of the IJCCC article;
  • Retain the copyright notices and links to these terms and conditions so it is clear to other users what can and what cannot be done with the  article;
  • Ensure that, for any content in the IJCCC article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party;
  • Any translations must prominently display the statement: "This is an unofficial translation of an article that appeared in IJCCC. Agora University  has not endorsed this translation."

This is a non commercial license where the use of published articles for commercial purposes is forbiden. 

Commercial purposes include: 

  • Copying or downloading IJCCC articles, or linking to such postings, for further redistribution, sale or licensing, for a fee;
  • Copying, downloading or posting by a site or service that incorporates advertising with such content;
  • The inclusion or incorporation of article content in other works or services (other than normal quotations with an appropriate citation) that is then available for sale or licensing, for a fee;
  • Use of IJCCC articles or article content (other than normal quotations with appropriate citation) by for-profit organizations for promotional purposes, whether for a fee or otherwise;
  • Use for the purposes of monetary reward by means of sale, resale, license, loan, transfer or other form of commercial exploitation;

    The licensor cannot revoke these freedoms as long as you follow the license terms.

[End of CC-BY-NC  License for Website User]

INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL (IJCCC), With Emphasis on the Integration of Three Technologies (C & C & C),  ISSN 1841-9836.

IJCCC was founded in 2006,  at Agora University, by  Ioan DZITAC (Editor-in-Chief),  Florin Gheorghe FILIP (Editor-in-Chief), and  Misu-Jan MANOLESCU (Managing Editor).

Ethics: This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE).

Ioan  DZITAC (Editor-in-Chief) at COPE European Seminar, Bruxelles, 2015:

IJCCC is covered/indexed/abstracted in Science Citation Index Expanded (since vol.1(S),  2006); JCR2018: IF=1.585..

IJCCC is indexed in Scopus from 2008 (CiteScore2018 = 1.56):

Nomination by Elsevier for Journal Excellence Award Romania 2015 (SNIP2014 = 1.029): Elsevier/ Scopus

IJCCC was nominated by Elsevier for Journal Excellence Award - "Scopus Awards Romania 2015" (SNIP2014 = 1.029).

IJCCC is in Top 3 of 157 Romanian journals indexed by Scopus (in all fields) and No.1 in Computer Science field by Elsevier/ Scopus.


 Impact Factor in JCR2018 (Clarivate Analytics/SCI Expanded/ISI Web of Science): IF=1.585 (Q3). Scopus: CiteScore2018=1.56 (Q2);

SCImago Journal & Country Rank

Editors-in-Chief: Ioan DZITAC & Florin Gheorghe FILIP.