Skip to main content
SpringerLink
Log in

Representation of Uncertainty with Information and Probabilistic Information Granules

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

Linguistic representations by human brain are often characterized with an intertwined combination of imprecision (due to incomplete knowledge), vagueness, or uncertainty. A powerful framework of information and probabilistic information granules is proposed to model this combination of different facets of uncertainty in natural representations without distortion of the underlying meaning. The proposed notions are deployed in formulation of a comprehensive approach to model complex uncertain situations involving imprecise/inexact probabilities of fuzzy events. The concepts are based upon the principle of information granulation that can be viewed as a human way of achieving data compression. The proposed approach closely resembles the implementation of the strategy of divide-and-conquer which brings it close to human problem-solving thought process. The study also makes an attempt to minimize distortion of information in its representation by fuzzy logic.

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

References

  1. Dubois, D., Prade, H.: Formal representations of uncertainty. In: Bouyssou, D., Dubois, D., Pirlot, M., Prade, H. (eds.) Decision-Making Process- Concepts and Methods, Chap. 3, pp. 85–156. ISTE London & Wiley, New York (2009)

    Chapter  Google Scholar 

  2. Agarwal, M., Biswas, K.K., Hanmandlu, M.: Fuzzy model building using probabilistic rules. In: IJCCI (FCTA) 2011, International Conference on Fuzzy Computation Theory and Applications, Scitepress, pp. 361–369, 24–26 Oct (2011)

  3. Yager, R.R.: A note on probabilities of fuzzy events. Inf. Sci. 18(2), 113–129 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23, 421–427 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  5. Yager, R.R.: A note on probabilities of fuzzy events. Inf. Sci. 18, 113–122 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kacprzyk, J.: Control of stochastic system in fuzzy environment with Yager’s probability of fuzzy event. Busefal 12, 77–89 (1982)

    MATH  Google Scholar 

  7. Kacprzyk, J.: Yager’s probability of fuzzy event in stochastic control under fuzziness. Tech. Report #MII-245, Iona College (1982)

  8. Klement, E.P.: Some remarks on a paper of R.R. Yager. Inf. Sci. 27, 211–220 (1982)

    Article  MATH  Google Scholar 

  9. Zadeh, L.A.: Fuzzy probabilities. Inf. Process. Manag. 20(3), 363–372 (1984)

    Article  MATH  Google Scholar 

  10. Zadeh, L.A.: Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. J. Stat. Plan. Inference 105(1), 233–264 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zadeh, L.A.: Toward a generalized theory of uncertainty (GTU)—an outline. Inf. Sci. 172(1–2), 1–40 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zadeh, L.A.: Generalized theory of uncertainty (GTU)—principal concepts and ideas. Comput. Stat. Data Anal. 51(1), 15–46 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 90(2), 111–127 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pedrycz, W., Succi, G., Sillitti, A., Iljazi, J.: Data description: a general framework of information granules. Knowl. Based Syst. 80, 98–108 (2015)

    Article  Google Scholar 

  15. Wu, W.Z., Yang, X.P.: Information granules and approximations in incomplete information systems. In: 2007 International Conference on Machine Learning and Cybernetics, Hong Kong, pp. 3740–3745 (2007)

  16. Tsumoto, S., Hirano, S.: Information granules of statistical dependence in multiway contingency tables. In: Granular Computing (GrC), 2010 IEEE International Conference on, San Jose, CA, pp. 483–488 (2010)

  17. Wu, C., Yang, X.: Information granules in general and complete coverings. In: 2005 IEEE International Conference on Granular Computing, vol. 2, pp. 675–678 (2005)

  18. Hao, Y.B., Guo, X., Yang, N.D.: Research on information system attribute set information granules based on functional dependency. Wavelet Active Media Technology and Information Processing (ICCWAMTIP), 2014 11th International Computer Conference on, Chengdu, pp. 64–67 (2014)

  19. Walley, P., de Cooman, G.: A behavioral model for linguistic uncertainty. Inf. Sci. 134(1–4), 1–37 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1(1), 3–28 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  21. Yager, R.R.: A foundation for a theory of possibility. J. Cybern. 10, 177–204 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  22. Dubois, Didier: Possibility theory and statistical reasoning. Comput. Stat. Data Anal. 51(1), 47–69 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  23. Dubois, D., Prade, H.: Fuzzy sets and statistical data. Eur. J. Oper. Res. 25, 345–356 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  24. Dubois, D., Prade, H.: Evidence, knowledge, and belief functions. Int. J. Approx. Reason. 6(3), 295–319 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yager, R.R.: A representation of the probability of a fuzzy subset. Fuzzy Sets Syst. 13(3), 273–283 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  26. Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23(2), 421–427 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  27. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379–423 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  28. Universal Gambling Schemes and the Complexity Measures of Kolmogorov and Chaitin. Thomas M. Cover. Technical Report No. 12, Statistics Department, Stanford University (1974)

  29. Chaitin, G.: Randomness and mathematical proof. Sci. Am. 232(5), 46–52 (1975)

    Article  Google Scholar 

  30. Smets, P.: Probability of a fuzzy event: an axiomatic approach. Fuzzy Sets Syst. 7(2), 153–164 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  31. Zadeh, L.A.: From computing with numbers to computing with words. From manipulation of measurements to manipulation of perceptions. Circuits Syst. I 46(1), 105–119 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  32. Yager, R.R.: Probabilities from fuzzy observations. Inf. Sci. 32(1), 1–31 (1984)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Indian Institute of Management Ahmedabad, Ahmedabad, India

    Manish Aggarwal

Authors
  1. Manish Aggarwal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manish Aggarwal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aggarwal, M. Representation of Uncertainty with Information and Probabilistic Information Granules. Int. J. Fuzzy Syst. 19, 1617–1634 (2017). https://doi.org/10.1007/s40815-016-0242-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-016-0242-5

Keywords

Search

Navigation