Skip to main content
Log in

Random sets: A unified framework for multisource information fusion

  • Published:
Journal of Electronics (China)

Abstract

The more diverse the ways and means of information acquisition are, the more complex and various the types of information are. The qualities of available information are usually uncertain, vague, imprecise, incomplete, and so on. However, the information is modeled and fused traditionally in particular, name some of the known theories: evidential, fuzzy sets, possibilistic, rough sets or conditional events, etc. For several years, researchers have explored the unification of theories enabling the fusion of multisource information and have finally considered random set theory as a powerful mathematical tool. This paper attempts to overall review the close relationships between random set theory and other theories, and introduce recent research results which present how different types of information can be dealt with in this unified framework. Finally, some possible future directions are discussed.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Mihai. C. Florea, Anne-Laure Jousselme, Dominic Grenier, and Eloi Bosse. An unified approach to the fusion of imperfect data. Proceedings of SPIE, 4731(2000), 75–85.

    Google Scholar 

  2. Xu Xiaobin, Wen Chenglin, and Liu Rongli. The unified method of describing multisource information based on random set theory. Acta Electronica Sinica 36(2008)6, 1–7 (in Chinese). 徐晓滨, 文成林, 刘荣利. 多源信息基于随机集理论的统一表示与建模方法. 电子学报, 36(2008)6, 1–7.

    Article  MATH  Google Scholar 

  3. I. R. Goodman, R. Mahler, et al. Mathematics of Data Fusion. Kluwer Academic Publishers, Netherlands, 1997, 28–44.

    MATH  Google Scholar 

  4. P. Smets. Imperfect information: imprecision-uncertainty. Uncertainty Management in Information Systems from Needs to Solutions. Kluwer Academic Publishers, Netherlands, 1997, 225–254.

    Google Scholar 

  5. Zdzisıaw Pawlak and Andrzej Skowron. Rudiments of rough sets. Information Sciences, 177(2007)1, 3–27.

    Article  MATH  MathSciNet  Google Scholar 

  6. L. A. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 100(1999)26, 9–34.

    Article  MathSciNet  Google Scholar 

  7. H. T. Nguyen. An Introduction to Random Sets. CRC Press, USA, 2006, 4–10.

    Book  MATH  Google Scholar 

  8. R. Mahler. Random sets: unification and computation for information fusion a retrospective assessment. The 7th International Conference on Information Fusion, 2004, Sweden, 1–20.

  9. D. G. Kendall. Foundation of a theory of ransom sets. Stochastic Geometry, John Wiley, New Youk, 1974, 322–376.

    Google Scholar 

  10. R. P. Mahler. Random sets in information fusion an overview. Random Sets: Theory and Applications, Springer, 1997, USA, 129–164.

    Google Scholar 

  11. V. Kreinovich. Random sets unify, explain, and aid known uncertainty methods in expert systems. Random Sets: Theory and Applications, Springer, 1997, USA, 321–345.

    Google Scholar 

  12. G. Shafer. A mathematical theory of evidence. Princeton University Press, 1976, USA, 1–100.

    MATH  Google Scholar 

  13. H. T. Nguyen. On random sets and belief functions. Journal of Mathematical Analysis and Applications, 65(1978), 531–542.

    Article  MATH  MathSciNet  Google Scholar 

  14. Yunmin Zhu and X. Rong Li. Extended Dempster-Shafer combination rules based on random set theory. Proceedings of SPIE, 5434(2004), 112–120.

    Article  Google Scholar 

  15. Wen Chenglin, Xu Xiaobin, and Li Zhiliang. Research on unified description and extension of combination rules of evidence based on random set theory. Chinese Journal of Electronics, 17(2008)2, 279–284.

    Google Scholar 

  16. R. Mahler, J. Leavitt, et al.. Nonlinear filtering with really bad data, In Part of the SPIE Conference on Signal Processing, Sensor Fusion, and Target Recognition. SPIE, America, 2001, 59–70.

    Google Scholar 

  17. Xu Xiaobin, Wen Chenglin, and Wang Yingchang. Information fusion algorithm of fault diagnosis based on random set metrics of fuzzy fault features. Journal of Electronics & Information Technology, 31(2009)7, 1635–1640 (in Chinese). 徐晓滨, 文成林, 王迎昌. 基于模糊故障特征信息的随机集度量信息融合诊断方法. 电子与信息学报, 31 (2009)7, 1635–1640.

    Google Scholar 

  18. Mihai C. Florea, Anne-Laure Jousselme, Dominic Grenier, et al.. Approximation techniques for the transformation of fuzzy sets into random sets. Fuzzy Set and Systems, 159(2008)3, 270–288.

    Article  MATH  MathSciNet  Google Scholar 

  19. I. R. Goodman. Fuzzy sets as equivalence classes of possibility random sets. Fuzzy Sets and Possibility Theory: Recent Developments, Pergamon Oxford Press, 1982, New York, 327–343.

    Google Scholar 

  20. I. R. Goodman, H. T. Nguyen, and E. A. Walker. Conditional Inference and Logic for Intelligent Systems: A Theory of Measure-free Conditioning. Amsterdam North-Holland Press, 1991, New York, 55–60.

    Google Scholar 

  21. I. R. Goodman and G. F. Kramer. Extension of relational and conditional event algebra to random sets with applications to data fusion. Random sets: Theory and Applications, Springer, New York, 1997, 209–243.

    Google Scholar 

  22. Z. Pawlak. Rough Sets-theorical Aspects of Reasoning about Data. Kluwer Academic Publisher, 1991, 89–90.

  23. Zhang Wenxiu and Wu Zhiwei. The rough set model based on random sets(?). Journal of Xi’an Jiaotong University, 34(2000)12, 76–79 (in Chinese). 张文修, 吴伟志. 基于随机集的粗糙集模型(I). 西安交通大学学报, 34(2000)12, 76–79.

    Google Scholar 

  24. Zhang Wenxiu and Wu Zhiwei. The rough set model based on random sets(II). Journal of Xi’an Jiaotong University, 35(2001)4, 425–429 (in Chinese). 张文修, 吴伟志. 基于随机集的粗糙集模型(II). 西安交通大学学报, 35(2001)4, 425–429.

    MathSciNet  Google Scholar 

  25. Peng Dongliang, Wen Chenglin, Xu Xiaobin, and Xue Anke. Random set and its application in information fusion. Journal of Electronic & Information Technology, 28(2006)11, 2199–2204 (in Chinese). 彭冬亮, 文成林, 徐晓滨, 薛安克. 随机集理论及其在信息融合中的应用. 电子与信息学报, 28(2006)11, 2199–2204.

    Google Scholar 

  26. R. P. S. Mahler. Multitarget Bayes filtering via first-order multi-target moments. IEEE Transactions on Aerospace and Electronic Systems, 39(2003)4, 1152–1178.

    Article  Google Scholar 

  27. E. Biglieri and M. Lops. Multiuser detection in a dynamic environment. Part I: User identification and data detection. IEEE Transations on Inform Theory, 52(2007)9, 3158–3170.

    Article  MathSciNet  Google Scholar 

  28. F. Tonon, A. Bernardini, and A. Mammino. Determination of parameters in rock engineering by means of random set theory. Reliability Engineering and System Safety, 70(2000), 241–261.

    Article  Google Scholar 

  29. Javier Nunez-Garcia and Olaf Wolkenhauer. Random set system identification. IEEE Transactions on Fuzzy Systems, 10(2002)3, 287–296.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiaobin Xu.

Additional information

Supported in part by the NSFC (No.60934009,60874105) and the ZJNSF (Y1080422, R106745), NCET (08-0345)

Communication author: Xu Xiaobin, born in 1980, male, Ph.D..

About this article

Cite this article

Xu, X., Wen, C. Random sets: A unified framework for multisource information fusion. J. Electron.(China) 26, 723–730 (2009). https://doi.org/10.1007/s11767-009-0085-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11767-009-0085-4

Key words

CLC index

Navigation