Generalized Ordered Propositions Fusion Based on Belief Entropy

Yangxue Li, Yong Deng


A set of ordered propositions describe the different intensities of a characteristic of an object, the intensities increase or decrease gradually. A basic support function is a set of truth-values of ordered propositions, it includes the determinate part and indeterminate part. The indeterminate part of a basic support function indicates uncertainty about all ordered propositions. In this paper, we propose generalized ordered propositions by extending the basic support function for power set of ordered propositions. We also present the entropy which is a measure of uncertainty of a basic support function based on belief entropy. The fusion method of generalized ordered proposition also be presented. The generalized ordered propositions will be degenerated as the classical ordered propositions in that when the truth-values of non-single subsets of ordered propositions are zero. Some numerical examples are used to illustrate the efficiency of generalized ordered propositions and their fusion.


ordered proposition; Dempster-Shafer evidence theory; uncertainty measure; belief entropy; information fusion

Full Text:



W. Feller. (2008); An introduction to probability theory and its applications, Vol. 2, John Wiley & Sons, 2008.

A. P. Dempster. (1967); Upper and lower probabilities induced by a multivalued mapping, The annals of mathematical statistics, (1967) 325–339.

G. Shafer, et al. (1976); A mathematical theory of evidence, Vol. 1, Princeton university press Princeton, 1976.

Z. Pawlak, J. Grzymala-Busse, R. Slowinski, W. Ziarko. (1995) Rough sets, Communications of the ACM 38 (11) (1995) 88–95.

L. A. Zadeh. (1996) ; Fuzzy sets, in: Fuzzy Sets, Fuzzy Logic, And Fuzzy Systems: Selected Papers by Lotfi A Zadeh, World Scientisc, 1996, pp. 394–432.

R. Zhang, X. Ran, C. Wang, Y. Deng. (2016); Fuzzy Evaluation of Network Vulnerability, Quality and Reliability Engineering International, 32 (5) (2016) 1715–1730.

J. H. Dahooie, E. K. Zavadskas, M. Abolhasani, A. Vanaki, Z. Turskis. (2018); A novel approach for evaluation of projects using an interval valued fuzzy additive ratio assessment ARAS method: A case study of oil and gas well drilling projects, Symmetry, 10 (2) (2018) 45.

M. Azadi, M. Jafarian, R. F. Saen, S. M. Mirhedayatian. (2014); A new fuzzy dea model for evaluation of eficiency and effectiveness of suppliers in sustainable supply chain management context, Computers & Operations Research, 54 (2014) 274–285.

Y. T. Liu, N. R. Pal, A. R. Marathe, C. T. Lin. (2018); Weighted fuzzy dempster-shafer framework for multimodal information integration, IEEE Transactions on Fuzzy Systems, 26 (1) (2018) 338–352.

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.

Bogdana Stanojevi and Ioan Dziac and Simona Dziac,(2015); On the ratio of fuzzy numbers exact membership function computation and applications to decision making, Technological and Economic Development of Economy, (2015) 21(5) 815-832.

L. A. Zadeh. (2011); A note on z-numbers, Information Sciences, 181 (14) (2011) 2923–2932.

B. Kang, G. Chhipi-Shrestha, Y. Deng, K. Hewage, R. Sadiq. (2018); Stable strategies analysis based on the utility of Z-number in the evolutionary games, Applied Mathematics & Computation, 324 (2018) 202–217.

T. Bian, H. Zheng, L. Yin, Y. Deng. (2018); Failure mode and effects analysis based on D numbers and topsis, Quality and Reliability Engineering International, (2018) Article ID: QRE2268

F. Xiao. (2016); An intelligent complex event processing with D numbers under fuzzy environment, Mathematical Problems in Engineering, 2016 (1) (2016) 1–10.

D. Liu, Y. Zhu, N. Ni, J. Liu. (2017); Ordered proposition fusion based on consistency and uncertainty measurements, Science China Information Sciences, 60 (8) (2017) 082103.

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

Q. Zhang, M. Li, Y. Deng. (2018); Measure the structure similarity of nodes in complex networks based on relative entropy, Physica A: Statistical Mechanics and its Applications, 491 (2018) 749–763.

L. Yin, Y. Deng. (2018); Measuring transferring similarity via local information, Physica A: Statistical Mechanics and its Applications, (2018).

X. Zheng, Y. Deng.(2018); Dependence assessment in human reliability analysis based on evidence credibility decay model and iowa operator, Annals of Nuclear Energy, 112 (2018) 673–684.

X. Deng, Y. Deng. (2018); D-AHP method with different credibility of information, Soft Computing (2018) Published online,

C. Fu, J.-B. Yang, S.-L. Yang. (2015); A group evidential reasoning approach based on expert reliability, European Journal of Operational Research, 246 (3) (2015) 886–893.

X. Zhang, S. Mahadevan, X. Deng. (2017); Reliability analysis with linguistic data: An evidential network approach, Reliability Engineering & System Safety, 162 (2017) 111–121.

Yuan, R., Meng, D., and Li, H. (2016); Multidisciplinary reliability design optimization using an enhanced saddlepoint approximation in the framework of sequential optimization and reliability analysis, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 230(6), 570-578.

Meng, D., Zhang, H., Huang, T. (2016); A concurrent reliability optimization procedure in the earlier design phases of complex engineering systems under epistemic uncertainties, Advances in Mechanical Engineering, 8(10), 1687814016673976.

Chao, X. R., Kou, G., Peng, Y. (2017); A Similarity Measure-based Optimization Model for Group Decision Making with Multiplicative and Fuzzy Preference Relations. International

Journal of Computers, Communications & Control, 12(1).

Y. Li, J. Chen, F. Ye, D. Liu; The Improvement of DS Evidence Theory and Its Application in IR/MMW Target Recognition, Journal of Sensors, (1903792).

Li, Y., Chen, J., Ye, F., Liu, D. (2016); The improvement of DS evidence theory and its application in IR/MMW target recognition, Journal of Sensors, 2016.

L. Chen, X. Deng. (2018); A modfied method for evaluating sustainable transport solutions based on ahp and dempstercshafer evidence theory, Applied Sciences, 8 (4) (2018) Article ID 563.

C. Fu, S. Yang. (2014); Conjunctive combination of belief functions from dependent sources using positive and negative weight functions, Expert Systems with Applications, 41 (4) (2014) 1964–1972.

Y. Zhao, R. Jia, P. Shi, (2016). A novel combination method for conflicting evidence based on inconsistent measurements, Information Sciences, 367–368 (2016) 125–142.

Z. Liu, Q. Pan, J. Dezert, A. Martin. (2017); Combination of classifiers with optimal weight based on evidential reasoning, IEEE Transactions on Fuzzy Systems, PP (99) (2017) 1–15.

H. Xu, Y. Deng. (2018); Dependent evidence combination based on shearman coefficient

and pearson coeflicient, IEEE Access, (2018) 10.1109/ACCESS.2017.2783320.

H. Zheng, Y. Deng. (2017); Evaluation method based on fuzzy relations between Dempster Shafer belief structure, International Journal of Intelligent Systems, (2017)

K.-S. Chin, C. Fu. (2015); Weighted cautious conjunctive rule for belief functions combination, Information Sciences, 325 (2015) 70–86.

W. Bi, A. Zhang, Y. Yuan. (2017); Combination method of conflict evidences based on evidence similarity, Journal of Systems Engineering and Electronics, 28 (3) (2017) 503–513.

Y. Song, X. Wang, L. Lei, Y. Xing. (2015); Credibility decay model in temporal evidence combination, Information Processing Letters, 115 (2) (2015) 248–252.

W. Jiang, S. Wang, X. Liu, H. Zheng, B. Wei. (2017); Evidence confict measure based on OWA operator in open world, PloS one, 12 (5) (2017) e0177828.

R. R. Yager, P. Elmore, F. Petry. (2017); Soft likelihood functions in combining evidence, Information Fusion, 36 (2017) 185–190.

Jiang, W., Yang, Y., Luo, Y., Qin, X. (2015); Determining basic probability assignment based on the improved similarity measures of generalized fuzzy numbers, International Journal of Computers Communications & Control, 10(3), 333-347.

K. Chatterjee, E. K. Zavadskas, J. Tamoaitien, K. Adhikary, S. Kar. (2018); A hybrid mcdm technique for risk management in construction projects, Symmetry, 10 (2) (2018) 46.

W. Jiang, C. Xie, M. Zhuang, Y. Tang. (2017); Failure mode and effects analysis based on a novel fuzzy evidential method, Applied Soft Computing, 57 (2017) 672–683.

Y. Gong, X. Su, H. Qian, N. Yang. (2017); Research on fault diagnosis methods for the reactor coolant system of nuclear power plant based on D-S evidence theory, Annals of Nuclear Energy, (2017)

F. Li, X. Zhang, X. Chen, Y. C. Tian. (2017); Adaptive and robust evidence theory with applications in prediction of floor water inrush in coal mine, Transactions of the Institute of Measurement & Control, 39 (1) (2017) 014233121668781.

F. Xiao. (2017); A novel evidence theory and fuzzy preference approach-based multi-sensor data fusion technique for fault diagnosis, Sensors, 17 (11) (2017) 2504.

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

F. Xiao. (2017); An improved method for combining conficting evidences based on the similarity measure and belief function entropy, International Journal of Fuzzy Systems, (2017)

X. Deng. (2018); Analyzing the monotonicity of belief interval based uncertainty measures in belief function theory, International Journal of Intelligent Systems (2018) Published online.

V. Huynh, Y. Nakamori, T. Ho, T. Murai. (2006); Multiple-attribute decision making under uncertainty: The evidential reasoning approach revisited, IEEE Transaction on Systems Man and Cybernetics Part A-Systems and Humans, 36 (4) (2006) 804–822.

X. Zhang, S. (2017); Mahadevan, Aircraft re-routing optimization and performance assessment under uncertainty, Decision Support Systems, 96 (2017) 67–82.

X. Zhang, S. Mahadevan. (2017); A game theoretic approach to network reliability assessment, IEEE Transactions on Reliability, 66 (3) (2017) 875–892.

Zhang, X., Mahadevan, S., Sankararaman, S., and Goebel, K. (2018); Resilience-based network design under uncertainty, Reliability Engineering & System Safety, 169, 364-379.

Y. Duan, Y. Cai, Z. Wang, X. Deng.(2018); A novel network security risk assessment approach by combining subjective and objective weights under uncertainty, Applied Sciences, 8 (3) (2018) Article ID 428.

R. R. Yager. (2016); Uncertainty modeling using fuzzy measures, Knowledge-Based Systems, 92 (2016) 1–8.

C. Li, S. Mahadevan. (2016); Relative contributions of aleatory and epistemic uncertainty sources in time series prediction, International Journal of Fatigue , 82 (2016) 474–486.

R. R. Yager. (2016); On viewing fuzzy measures as fuzzy subsets, IEEE Transactions on Fuzzy Systems, 24 (4) (2016) 811–818.

C. Li, S. Mahadevan . (2016); Role of calibration, validation, and relevance in multi-level uncertainty integration, Reliability Engineering & System Safety, 148 (2016) 32–43.

W. Jiang, S. Wang. (2017); An uncertainty measure for interval-valued evidences, International Journal of Computers Communications & Control, 12 (5) (2017) 631–644.

O. Mohsen, N. Fereshteh. (2017), An extended vikor method based on entropy measure for the failure modes risk assessmenta case study of the geothermal power plant (gpp), Safety Science, 92 (2017) 160–172.

F. Sabahi. (2016); A novel generalized belief structure comprising unprecisiated uncertainty applied to aphasia diagnosis, Journal of Biomedical Informatics, 62 (2016) 66–77.

J. Abelln. (2017); Analyzing properties of deng entropy in the theory of evidence, Chaos Solitons & Fractals, 95 (2017) 195–199.


Copyright (c) 2018 Yangxue Li, 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); JCR2016: IF=1.374. .

IJCCC is indexed in Scopus from 2008 (CiteScore 2017 = 1.04; SNIP2017 = 0.616, SJR2017 =0.326):

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.