Fusion of imprecise qualitative information | Applied Intelligence Skip to main content
Springer Nature Link
Log in

Fusion of imprecise qualitative information

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

In this paper, we present a new 2-tuple linguistic representation model, i.e. Distribution Function Model (DFM), for combining imprecise qualitative information using fusion rules drawn from Dezert-Smarandache Theory (DSmT) framework. Such new approach allows to preserve the precision and efficiency of the combination of linguistic information in the case of either equidistant or unbalanced label model. Some basic operators on imprecise 2-tuple labels are presented together with their extensions for imprecise 2-tuple labels. We also give simple examples to show how precise and imprecise qualitative information can be combined for reasoning under uncertainty. It is concluded that DSmT can deal efficiently with both precise and imprecise quantitative and qualitative beliefs, which extends the scope of this theory.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Denœux T (1999) Reasoning with imprecise belief structures. Int J Approx Reas 20:79–111 (published preliminary as Heudiasys 97/44 Technical Report)

    MATH  Google Scholar 

  2. Dezert J, Smarandache F (2004) Fusion of imprecise beliefs. In: Smarandache F, Dezert J (eds) Advances and applications of DSmT for information fusion (collected works), vol 1. American Research Press, Rehoboth.

    Google Scholar 

  3. Dezert J, Smarandache F (2008) A new probabilistic transformation of belief mass assignment. In: Proceedings of fusion 2008 international conference, Cologne, Germany, July 2008

  4. Dubois D, Prade H (2001) Decision-theoretic foundations of qualitative possibility theory. Eur J Oper Res 128(3):459–478

    Article  MATH  MathSciNet  Google Scholar 

  5. Dubois D, Prade H (1993) Qualitative reasoning with imprecise probabilities. J Intell Inf Syst 2(4):319–363

    Article  Google Scholar 

  6. Ferson S, Donald S (1998) Probability bounds analysis. In: Proceedings of international conference on probabilistic safety assessment and management (PSAM4). Springer, New York

    Google Scholar 

  7. Wang J-H, Hao JY (2006) A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 14(3):435–445

    Article  Google Scholar 

  8. Wang J-H, Hao JY (2007) An approach to computing with words based on canonical characteristic values of linguistic labels. IEEE Trans Fuzzy Syst 15(4):593–603

    Article  Google Scholar 

  9. Hájek P, Harmancová D, Verbrugge R (1995) A qualitative fuzzy possibilistic logic. Int J Approx Reas 12(1):1–19

    Article  MATH  Google Scholar 

  10. Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752

    Article  Google Scholar 

  11. Herrera F, Martínez L (2001) A model based on linguistic 2-tuples for dealing with multi-granular hierarchical linguistic contexts in multi-expert decision-making. IEEE Trans Syst Man Cybern 31(2):227–234

    Article  Google Scholar 

  12. Herrera F, Herrera-Viedma E, Martínez L (2008) A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Trans Fuzzy Syst 16(2):354–370

    Article  Google Scholar 

  13. Li X (2007) Research on fusion method of imperfect information from multi-source and its application. PhD thesis, Huazhong University of Science and Technology, China, June 2007

  14. Li X, Huang X, Dezert J, Smarandache F (2007) Enrichment of qualitative beliefs for reasoning under uncertainty. In: Proceedings of fusion 2007 international conference, Québec, Canada, July 2007

  15. Kifer M, Subrahmanian VS (1991) Theory of generalized annotated logic programs and its applications. J Log Program

  16. Parsons S (1993) Qualitative methods for reasoning under uncertainty. PhD thesis, Department of Electrical Engineering, Queen Mary and Westfield College

  17. Parsons S, Mamdani E (1993) Qualitative Dempster-Shafer theory. In: Proceedings of the third EMACS international workshop on qualitative reasoning and decision technologies, Barcelona, Spain

  18. Parsons S (1994) Some qualitative approaches to applying Dempster-Shafer theory. Inf Decis Technol 19:321–337

    Google Scholar 

  19. Polya G (1954) Patterns of plausible inference. Princeton University Press, Princeton

    MATH  Google Scholar 

  20. Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton

    MATH  Google Scholar 

  21. Smarandache F, Dezert J (eds) (2004) Advances and applications of DSmT for information fusion (collected works), vol 1. American Research Press, Rehoboth. http://www.gallup.unm.edu/~smarandache/DSmT-book1.pdf

    MATH  Google Scholar 

  22. Smarandache F, Dezert J (2005) Information fusion based on new proportional conflict redistribution rules. In: Proceedings of fusion 2005, Philadelphia, USA, July 2005

  23. Smarandache F, Dezert J (eds) (2006) Advances and applications of DSmT for information fusion (collected works), vol 2. American Research Press, Rehoboth. http://www.gallup.unm.edu/~smarandache/DSmT-book2.pdf

    MATH  Google Scholar 

  24. Smarandache F, Dezert J (eds) (2009) Advances and applications of DSmT for information fusion (Collected works), vol 3. American Research Press, Rehoboth

    MATH  Google Scholar 

  25. Smarandache F, Dezert J (eds) (2007) Qualitative belief conditioning rules (QBCR). In: Proceedings of fusion 2007 international conference, Québec, Canada, July 2007

  26. Smets P, Kennes R (1994) The transferable belief model. Artif Intell 66:191–243

    Article  MATH  MathSciNet  Google Scholar 

  27. Subrahmanian VS (1987) On the semantics of quantitative logic programs. In: Proceedings of the 4th IEEE symposium on logic programming

  28. Walley P (1991) Statistical reasoning with imprecise probabilities. Chapman and Hall, New York

    MATH  Google Scholar 

  29. Wellman MP (1994) Some varieties of qualitative probability. In: Proceedings of the 5th international conference on information processing and the management of uncertainty (IPMU 1994), Paris, France, July 1994

  30. Yager RR (2004) On the retranslation process in Zadeh’s paradigm of computing with words. IEEE Trans Syst Man Cybern 34(2):1184–1195

    Article  Google Scholar 

  31. Zadeh L (1975) Concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8(1):199–249

    Article  MathSciNet  Google Scholar 

  32. Zadeh L (1979) A theory of approximate reasoning. Mach Intell 9:149–194

    Google Scholar 

  33. Zadeh L (1996) Fuzzy logic = computing with words. IEEE Trans Fuzzy Syst 4(2):103–111

    Article  MathSciNet  Google Scholar 

  34. Zadeh L (1997) Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst 19:111–127

    Article  MathSciNet  Google Scholar 

  35. Zadeh L (1998) Some reflections on soft computing, granular computing and their roles in the conception, design and utilization of information/intelligent systems. Soft Comput 2:23–25

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Measurement and Control of CSE (School of Automation, Southeast University), Ministry of Education, Nanjing, 210096, China

    Xinde Li & Xianzhong Dai

  2. ONERA (The French Aerospace Lab.), 29 Avenue de la Division Leclerc, 92320, Châtillon, France

    Jean Dezert

  3. Chair of Math. & Sciences Dept., University of New Mexico, 200 College Road, Gallup, NM, 87301, USA

    Florentin Smarandache

Authors
  1. Xinde Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xianzhong Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jean Dezert
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Florentin Smarandache
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinde Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, X., Dai, X., Dezert, J. et al. Fusion of imprecise qualitative information. Appl Intell 33, 340–351 (2010). https://doi.org/10.1007/s10489-009-0170-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-009-0170-2

Keywords

Search

Navigation