Handling Fuzzy Models in the Probabilistic Domain

  • Manish Agarwal
  • Kanad K. Biswas
  • Madasu Hanmandlu
Part of the Studies in Computational Intelligence book series (SCI, volume 465)


This chapter extends the fuzzy models to the probabilistic domain using the probabilistic fuzzy rules with multiple outputs. The focus has been to effectively model the uncertainty in the real world situations using the extended fuzzy models. The extended fuzzy models capture both the aspects of uncertainty, vagueness and random occurence. We also look deeper into the concepts of fuzzy logic, possibility and probability that sets the background for laying out the mathematical framework for the extended fuzzy models. The net conditional probabilistic possibility is computed that forms the key ingredient in the extension of the fuzzy models. The proposed concepts are well illustrated through two case-studies of intelligent probabilistic fuzzy systems. The study paves the way for development of computationally intelligent systems that are able to represent the real world situations more realistically.


Probabilistic fuzzy rules Probability possibility Fuzzy models Decision making 


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  1. 1.
    Zadeh, L.A.: Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems 1, 3–28 (1978)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Dubois, D., Prade, H.: When upper probabilities are possibility measures. Fuzzy Sets and Systems 49, 65–74 (1992)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Dubois, D., Prade, H., Sandri, S.: On possibility/probability transformations. In: Lowen, R., Roubens, M. (eds.) Fuzzy Logic, pp. 103–112 (1993)Google Scholar
  4. 4.
    Roisenberg, M., Schoeninger, C., Silva, R.R.: A hybrid fuzzy-probabilistic system for risk analysis in petroleum exploration prospects. Expert Systems with Applications 36, 6282–6294, 103–112 (2009)CrossRefGoogle Scholar
  5. 5.
    De Cooman, G., Aeyels, D.: Supremum-preserving upper probabilities. Inform. Sci. 118, 173–212 (1999)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Walley, P., de Cooman, G.: A behavioural model for linguistic uncertainty. Inform. Sci. 134, 1–37 (1999a)CrossRefGoogle Scholar
  7. 7.
    Dubois, D., Prade, H.: On several representations of an uncertain body of evidence. In: Gupta, M.M., Sanchez, E. (eds.) Fuzzy Information and Decision Processes, pp. 167–181. North-Holland (1982)Google Scholar
  8. 8.
    Dubois, D.: Possibility theory and statistical reasoning. Computational Statistics & Data Analysis 51(1), 47–69 (2006)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Meghdadi, A.H., Akbarzadeh-T, M.-R.: Probabilistic fuzzy logic and probabilistic fuzzy systems. In: The 10th IEEE International Conference on Fuzzy Systems, vol. 3, pp. 1127–1130 (2001)Google Scholar
  10. 10.
    Van den Berg, J., Van den Bergh, W.M., Kaymak, U.: Probabilistic and statistical fuzzy set foundations of competitive exception learning. In: The 10th IEEE International Conference on Fuzzy Systems, vol. 2, pp. 1035–1038 (2001)Google Scholar
  11. 11.
    Van den Bergh, W.M., Kaymak, U., Van den Berg, J.: On the data-driven design of Takagi-Sugeno probabilistic furzy systems. In: Proceedings of the EUNlTE Conference, Portugal (2002)Google Scholar
  12. 12.
    Azeem, M.F., Hanmandlu, M., Ahmad, N.: Generalization of adaptive neuro-fuzzy inference systems. IEEE Transactions on Neural Networks 11(6), 1332–1346 (2000)CrossRefGoogle Scholar
  13. 13.
    Kosko, B.: Fuzzy Thinking: The New Science of Fuzzy Logic. Hyperion (1993)Google Scholar
  14. 14.
    Klir, G.J.: Fuzzy Sets: An Overview of Fundamentals, Applications and Personal Views. Beijing Normal University Press, Beijing (2000)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Manish Agarwal
    • 1
  • Kanad K. Biswas
    • 1
  • Madasu Hanmandlu
    • 1
  1. 1.Indian Institute of TechnologyNew DelhiIndia

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