Some Notes on Possibilistic Learning

  • J. Gebhardt
  • R. Kruse
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 363)


We outline a possibilistic learning method for structure identification from a database of samples. In comparison to the construction of Bayesian belief networks, the proposed framework has some advantages, namely the explicit consideration of imprecise data, and the realization of a controlled form of information compression in order to increase the efficiency of the learning strategy as well as approximate reasoning using local propagation techniques.

Our learning method has been applied to reconstruct a non-singly connected network of 22 nodes and 22 arcs without the need of any a priori supplied node ordering.


Belief Function Possibility Distribution Frame Condition Possibility Theory Approximate Reasoning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Zadeh, L.A.: Fuzzy Sets as a Basis for a Theory of Possibility, Fuzzy Sets and Systems, 1 (1978), 3–28.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    Dubois, D. and H. Prade: Possibility Theory, Plenum Press, New York 1988.CrossRefMATHGoogle Scholar
  3. [3]
    Strassen, V.: Meßfehler und Information, Zeitschrift Wahrscheinlichkeitstheorie und verwandte Gebiete, 2 (1964), 273–305.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Dempster, A.P.: Upper and Lower Probabilities Induced by a Random Closed Interval, Ann. Math. Stat., 39 (1968), 957–966.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Kampé de Fériet, J.: Interpretation of Membership Functions of Fuzzy Sets in Terms of Plausibility and Belief, in: Fuzzy Information and Decision Processes (Ed. M.M. Gupta, E. Sanchez ), North-Holland, 1982, 13–98.Google Scholar
  6. [6]
    Gebhardt, J. and R. Kruse: The Context Model–An Integrating View of Vagueness and Uncertainty, Int. J. of Approximate Reasoning, 9 (1993), 283–314.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    Gebhardt, J. and R. Kruse: A Comparative Discussion of Combination Rules in Numerical Settings, CEC-ESPRIT III BRA 6156 DRUMS II, Annual Report, 1993.Google Scholar
  8. [8]
    Nguyen, H.T.: On Random Sets and Belief Functions, J. of Mathematical Analysis and Applications, 65 (1978), 531–542.CrossRefMATHGoogle Scholar
  9. [9]
    Shafer, G.: A Mathematical Theory of Evidence, Princeton University Press, Princeton 1976.Google Scholar
  10. [10]
    Wang, P.Z.: From the Fuzzy Statistics to the Falling Random Subsets, in: Advances in Fuzzy Sets, Possibility and Applications (Ed. P.P. Wang ), Plenum Press, New York 1983, 81–96.CrossRefGoogle Scholar
  11. [11]
    Gebhardt, J. and R. Kruse: A New Approach to Semantic Aspects of Possihilistic Reasoning, in: Symbolic and Quantitative Approaches to Reasoning and Uncertainty (Ed. M. Clarke, R. Kruse, and S. Moral), Lecture Notes in Computer Science, 747 (1993), Springer, Berlin, 151–160.Google Scholar
  12. [12]
    Gebhardt, J. and R. Kruse: On an Information Compression View of Possibility Theory, in: Proc. 3rd IEEE Int. Conf. on Fuzzy Systems, Orlando 1994.Google Scholar
  13. [13]
    Pearl, J. and N. Wermuth: When Can Association Graphs Admit a Causal Interpretation (First Report), in: Preliminary Papers of the 4th Int. Workshop on Artificial Intelligence and Statistics, Ft. Lauderdale, FL January 3–6 1993, 141–1 51.Google Scholar
  14. [14]
    Verma, T. and J. Pearl: An Algorithm for Deciding if a Set of Observed Independencies Has a Causal Explanation, in: Proceedings 8th Conf. on Uncertainty in AI, 1992, 323–330.Google Scholar
  15. [15]
    Spirtes, P. and C. Glymour: An Algorithm for Fast Recovery of Sparse Causal Graphs, Social Science Computing Review, 9 (1991), 62–72.CrossRefGoogle Scholar
  16. [16]
    Cooper, C. and E. Herskovits: A Bayesian Method for the Induction of Probabilistic Networks from Data, Machine Learning, 9 (1992), 309–347.MATHGoogle Scholar
  17. [17]
    Lauritzen, S.L., B. Thiesson, and D. Spiegelhalter: Diagnostic Systems Created by Model Selection Methods — A Case Study, in: Preliminary Papers of the 4th Int. Workshop on Artificial Intelligence and Statistics, Ft. Lauderdale, FL January 3–6 1993, 141–151.Google Scholar
  18. [18]
    Singh, M. and M. Valtorta: An Algorithm for the Construction of Bayesian Network Structures from Data, in: Proc. 9th. Conf. on Uncertainty in Artificial Intelligence, Washington 1993, 259–265.Google Scholar
  19. [19]
    Dechter, R. and J. Pearl: Structure Identification in Relational Data, Artificial Intelligence, 58 (1992), 237–270.MathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    Hartley, R.V.L., Transmission of Information: The Bell Systems Technical J., 7 1928, 535–563.Google Scholar
  21. [21]
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems — Networks of Plausible Inference, Morgan Kaufman, San Mateo 1988.Google Scholar
  22. [22]
    Andersen, S.K., K.G. Olesen, F.V. Jensen, and F. Jensen: HUGIN — A Shell for Building Bayesian Belief Universes for Expert Systems, in: Proc. 11th Int. Joint Conf. on AI, 1989, 1080–1085.Google Scholar
  23. [23]
    Rasmussen, L.K.: Blood Group Determination of Danish Jersey Cattle in the F-blood Group System, Dina Research Report 8, Dina Foulum, 8830 Tjele, Denmark, November 1992.Google Scholar
  24. [24]
    Kruse, R., J. Gebhardt, and F. Klawonn: Foundations of Fuzzy Systems, Wiley, Chichester 1994.Google Scholar

Copyright information

© Springer-Verlag Wien 1995

Authors and Affiliations

  • J. Gebhardt
    • 1
  • R. Kruse
    • 1
  1. 1.University of BraunschweigBraunschweigGermany

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