Skip to main content
SpringerLink
Log in

A belief Sharma-Mittal divergence with its application in multi-sensor information fusion

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

Dempster-Shafer evidence theory (DSET) has a wide and important application in information fusion. However, when the pieces of evidence are highly conflicting, Dempster’s rule may lead to counter-intuitive results. To address this issue, a new enhanced belief Jensen-Sharma-Mittal (\(\mathcal {EBJSM}\)) divergence is proposed in this paper to measure the degree of conflict between the pieces of evidence. The \(\mathcal {EBJSM}\) divergence takes into account the influence of both single-element and multiple-element subsets. Furthermore, important properties of the \(\mathcal {EBJSM}\) divergence are explored and proved, including its non-negativity, non-degeneracy, symmetry and relationships with the belief Jensen-Tsallis divergence, the belief Jensen-Rényi divergence, the Kullback–Leibler divergence, the Hellinger distance and \(\chi ^2\) divergence. Based on the \(\mathcal {EBJSM}\) divergence and the improved belief entropy, a new multi-sensor information fusion method is designed. Finally, the proposed multi-sensor information fusion method is applied to several applications, and the practicality and effectiveness of the new method is verified. In particular, the proposed method achieved the best average classification accuracy of 0.9292 on the Iris dataset.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability

All data information is included in the paper.

Notes

  1. Although Sects. 5.2 and 5.3 both used the Iris dataset for experiments, the methods of generating mass functions in these two experiments are different. In addition, in Sect. 5.2, only one pattern are used for experiment, while in Sect. 5.3, we used the entire dataset for experiment.

References

  • Aggarwal M (2017) Rough information set and its applications in decision making. IEEE Trans Fuzzy Syst 25(2):265–276

    Article  Google Scholar 

  • Crooks GE (2017) On measures of entropy and information. Tech Note 9:4

    Google Scholar 

  • Dempster A (1967) Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat., 325–339

  • Deng Y, Shi W, Zhu Z, Liu Q (2004) Combining belief functions based on distance of evidence. Decis Support Syst 38(3):489–493

    Article  Google Scholar 

  • Dubois D, Prade H (1988) Representation and combination of uncertainty with belief functions and possibility measures. Comput Intell 4(3):244–264

    Article  Google Scholar 

  • Dubois D, Prade H (2001) Possibility theory, probability theory and multiple-valued logics: A clarification. Ann Math Artif Intell 32:35–66

    Article  MathSciNet  Google Scholar 

  • Gao X, Xiao F (2022) An improved belief \(\chi ^2\) divergence for dempster-shafer theory and its applications in pattern recognition. Comput Appl Math 41(6):277

    Article  MathSciNet  Google Scholar 

  • Garg H, Kumar K (2019) Linguistic interval-valued atanassov intuitionistic fuzzy sets and their applications to group decision-making problems. IEEE Trans. Fuzzy Syst., 1–1

  • Ghosh R, Kumar P, Roy PP (2019) A dempster-shafer theory based classifier combination for online signature recognition and verification systems. Int J Mach Learn Cybern 10:2467–2482

    Article  CAS  Google Scholar 

  • He Y, Deng Y (2022) Mmget: a markov model for generalized evidence theory. Comput Appl Math 41:1–41

    Article  MathSciNet  Google Scholar 

  • He Y, Xiao F (2022) A new base function in basic probability assignment for conflict management. Appl Intell 52(4):4473–4487

    Article  Google Scholar 

  • Huang C, Mi X, Kang B (2021) Basic probability assignment to probability distribution function based on the shapley value approach. Int J Intell Syst 36(8):4210–4236

    Article  Google Scholar 

  • Huang H, Liu Z, Han X, Yang X, Liu L (2023) A belief logarithmic similarity measure based on dempster-shafer theory and its application in multi-source data fusion. J Intell Fuzzy Syst 45(3):4935–4947

    Article  Google Scholar 

  • Islam SM, Wu T, Ledwich G (2000) A novel fuzzy logic approach to transformer fault diagnosis. IEEE Trans Dielectr Electr Insul 7(2):177–186

    Article  Google Scholar 

  • Jiang W (2018) A correlation coefficient for belief functions. Int J Approx Reason 103:94–106

    Article  MathSciNet  Google Scholar 

  • Kaur M, Srivastava A (2022) A new divergence measure for belief functions and its applications. Int. J. General Syst., 1–18

  • Lee H, Kwon H (2021) DBF: Dynamic belief fusion for combining multiple object detectors. IEEE Trans Pattern Anal Mach Intell 43(5):1499–1514

    Article  PubMed  Google Scholar 

  • Li Y, Pelusi D, Deng Y (2020) Generate two-dimensional belief function based on an improved similarity measure of trapezoidal fuzzy numbers. Comput Appl Math 39:1–20

    Article  MathSciNet  Google Scholar 

  • Li X, Liu Z, Han X, Liu N, Yuan W (2023) An intuitionistic fuzzy version of hellinger distance measure and its application to decision-making process. Symmetry 15(2):500

    Article  ADS  Google Scholar 

  • Lin Y, Li Y, Yin X, Dou Z (2018) Multisensor fault diagnosis modeling based on the evidence theory. IEEE Trans Reliab 67(2):513–521

    Article  Google Scholar 

  • Liu Z (2023) Credal-based fuzzy number data clustering. Granul Comput 8:1907–1924

    Article  Google Scholar 

  • Liu Z (2023) An effective conflict management method based on belief similarity measure and entropy for multi-sensor data fusion. Artif Intell Rev 56:15495–15522

    Article  Google Scholar 

  • Liu Z (2023) An evidential sine similarity measure for multisensor data fusion with its applications. Comput Granul. https://doi.org/10.1007/s41066-023-00426-6

    Article  Google Scholar 

  • Liu Z, Huang H (2023) Comment on “new cosine similarity and distance measures for fermatean fuzzy sets and topsis approach’’. Knowl Inf Syst 65:5151–5157

    Article  Google Scholar 

  • Liu P, Xiao F (2022) Earth mover’s divergence of belief function. Comput Appl Math 41(6):292

    Article  MathSciNet  Google Scholar 

  • Liu Z, Cao Y, Yang X, Liu L (2023) A new uncertainty measure via belief rényi entropy in dempster-shafer theory and its application to decision making. Commun. Stat. - Theory Methods, 1–20. https://doi.org/10.1080/03610926.2023.2253342

  • Liu Z, Huang H, Letchmunan S (2023) Adaptive weighted multi-view evidential clustering. In: Int. Conf. Artif. Neural Networks, pp. 265–277

  • Lu P, Zhou Y, Wu Y, Li D (2022) Risk assessment of complex footbridge based on dempster-shafer evidence theory using fuzzy matter-element method. Appl Soft Comput 131:109782

    Article  Google Scholar 

  • Ma Z, Liu Z, Luo C, Song L (2021) Evidential classification of incomplete instance based on k-nearest centroid neighbor. J Intell Fuzzy Syst 41(6):7101–7115

    Article  Google Scholar 

  • Murphy CK (2000) Combining belief functions when evidence conflicts. Decis Support Syst 29(1):1–9

    Article  CAS  Google Scholar 

  • Pan Y, Zhang L, Li Z, Ding L (2020) Improved fuzzy bayesian network-based risk analysis with interval-valued fuzzy sets and d-s evidence theory. IEEE Trans Fuzzy Syst 28(9):2063–2077

    Article  Google Scholar 

  • Shafer G (1976) A Mathematical Theory of Evidence, vol 42. Princeton University Press, Princeton

    Book  Google Scholar 

  • Sharma BD, Mittal DP (1975) New non-additive measures of entropy for discrete probability distributions. J Math Sci 10:28–40

    MathSciNet  Google Scholar 

  • Smets P (1990) The combination of evidence in the transferable belief model. IEEE Trans Pattern Anal Mach Intell 12(5):447–458

    Article  Google Scholar 

  • Wang H, Deng X, Jiang W, Geng J (2021) A new belief divergence measure for Dempster-Shafer theory based on belief and plausibility function and its application in multi-source data fusion. Eng Appl Artif Intell 97:104030

    Article  Google Scholar 

  • Xiao F (2019) Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy. Inf Fusion 46:23–32

    Article  Google Scholar 

  • Xiao F (2020) Generalized belief function in complex evidence theory. J Intell Fuzzy Syst 38(4):3665–3673

    Article  Google Scholar 

  • Xiao F (2022) Ceqd: A complex mass function to predict interference effects. IEEE Trans Cybern 52(8):7402–7414

    Article  PubMed  Google Scholar 

  • Xiao F (2022) GEJS: A generalized evidential divergence measure for multisource information fusion. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2022.3211498

    Article  Google Scholar 

  • Xiao F, Pedrycz W (2023) Negation of the quantum mass function for multisource quantum information fusion with its application to pattern classification. IEEE Trans Pattern Anal Mach Intell 45(2):2054–2070

    Article  PubMed  Google Scholar 

  • Xiao F, Cao Z, Jolfaei A (2021) A novel conflict measurement in decision-making and its application in fault diagnosis. IEEE Trans Fuzzy Syst 29(1):186–197

    Article  Google Scholar 

  • Xiao F, Wen J, Pedrycz W (2023) Generalized divergence-based decision making method with an application to pattern classification. IEEE Trans Knowl Data Eng 35(7):6941–6956

    Google Scholar 

  • Xiao F, Cao Z, Lin C-T (2023) A complex weighted discounting multisource information fusion with its application in pattern classification. EEE Trans Knowl Data Eng 35(8):7609–7623

    Google Scholar 

  • Yager RR (1987) On the dempster-shafer framework and new combination rules. Inf Sci 41(2):93–137

    Article  MathSciNet  Google Scholar 

  • Zhao K, Sun R, Li L, Hou M, Yuan G, Sun R (2021) An improved evidence fusion algorithm in multi-sensor systems. Appl. Intell., 1–11

  • Zhu S, Liu Z (2023) Distance measures of picture fuzzy sets and interval-valued picture fuzzy sets with their applications. AIMS Math 8(12):29817–29848

    Article  Google Scholar 

  • Zhu C, Xiao F (2023) A belief Rényi divergence for multi-source information fusion and its application in pattern recognition. Appl Intell 53(8):8941–8958

Download references

Funding

None.

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Hainan University, Haikou, 570228, China

    Shen Lyu

  2. School of Computer Sciences, Universiti Sains Malaysia, Penang, 11800, Malaysia

    Zhe Liu

Authors
  1. Shen Lyu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhe Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhe Liu.

Ethics declarations

Conflict of interest

The author declare that they have no conflict interest.

Ethics approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by Graçaliz Pereira Dimuro.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lyu, S., Liu, Z. A belief Sharma-Mittal divergence with its application in multi-sensor information fusion. Comp. Appl. Math. 43, 34 (2024). https://doi.org/10.1007/s40314-023-02542-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40314-023-02542-0

Keywords

Mathematics Subject Classification

Search

Navigation