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International Journal of Fuzzy Systems

, Volume 19, Issue 5, pp 1617–1634 | Cite as

Representation of Uncertainty with Information and Probabilistic Information Granules

Article

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.

Keywords

Imprecise probabilities Fuzzy sets Possibilistic uncertainty Information granules Modeling 

References

  1. 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)CrossRefGoogle Scholar
  2. 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)Google Scholar
  3. 3.
    Yager, R.R.: A note on probabilities of fuzzy events. Inf. Sci. 18(2), 113–129 (1979)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23, 421–427 (1968)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Yager, R.R.: A note on probabilities of fuzzy events. Inf. Sci. 18, 113–122 (1979)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Kacprzyk, J.: Control of stochastic system in fuzzy environment with Yager’s probability of fuzzy event. Busefal 12, 77–89 (1982)MATHGoogle Scholar
  7. 7.
    Kacprzyk, J.: Yager’s probability of fuzzy event in stochastic control under fuzziness. Tech. Report #MII-245, Iona College (1982)Google Scholar
  8. 8.
    Klement, E.P.: Some remarks on a paper of R.R. Yager. Inf. Sci. 27, 211–220 (1982)CrossRefMATHGoogle Scholar
  9. 9.
    Zadeh, L.A.: Fuzzy probabilities. Inf. Process. Manag. 20(3), 363–372 (1984)CrossRefMATHGoogle Scholar
  10. 10.
    Zadeh, L.A.: Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. J. Stat. Plan. Inference 105(1), 233–264 (2002)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Zadeh, L.A.: Toward a generalized theory of uncertainty (GTU)—an outline. Inf. Sci. 172(1–2), 1–40 (2005)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Zadeh, L.A.: Generalized theory of uncertainty (GTU)—principal concepts and ideas. Comput. Stat. Data Anal. 51(1), 15–46 (2006)MathSciNetCrossRefMATHGoogle Scholar
  13. 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)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Pedrycz, W., Succi, G., Sillitti, A., Iljazi, J.: Data description: a general framework of information granules. Knowl. Based Syst. 80, 98–108 (2015)CrossRefGoogle Scholar
  15. 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)Google Scholar
  16. 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)Google Scholar
  17. 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)Google Scholar
  18. 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)Google Scholar
  19. 19.
    Walley, P., de Cooman, G.: A behavioral model for linguistic uncertainty. Inf. Sci. 134(1–4), 1–37 (2001)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1(1), 3–28 (1978)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Yager, R.R.: A foundation for a theory of possibility. J. Cybern. 10, 177–204 (1980)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Dubois, Didier: Possibility theory and statistical reasoning. Comput. Stat. Data Anal. 51(1), 47–69 (2006)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Dubois, D., Prade, H.: Fuzzy sets and statistical data. Eur. J. Oper. Res. 25, 345–356 (1986)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Dubois, D., Prade, H.: Evidence, knowledge, and belief functions. Int. J. Approx. Reason. 6(3), 295–319 (1992)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Yager, R.R.: A representation of the probability of a fuzzy subset. Fuzzy Sets Syst. 13(3), 273–283 (1984)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23(2), 421–427 (1968)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379–423 (1948)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Universal Gambling Schemes and the Complexity Measures of Kolmogorov and Chaitin. Thomas M. Cover. Technical Report No. 12, Statistics Department, Stanford University (1974)Google Scholar
  29. 29.
    Chaitin, G.: Randomness and mathematical proof. Sci. Am. 232(5), 46–52 (1975)CrossRefGoogle Scholar
  30. 30.
    Smets, P.: Probability of a fuzzy event: an axiomatic approach. Fuzzy Sets Syst. 7(2), 153–164 (1982)MathSciNetCrossRefMATHGoogle Scholar
  31. 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)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Yager, R.R.: Probabilities from fuzzy observations. Inf. Sci. 32(1), 1–31 (1984)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Indian Institute of Management AhmedabadAhmedabadIndia

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