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A numerical framework for possibilistic abduction

  • Possibility Theory
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 945))

Abstract

We introduce a numerical framework for possibilistic abduction that is based on a relational setting for handling imprecise data and an information-compression view of possibility distributions as onepoint coverages of random sets. Existing dependencies among disorders, manifestations, and intermediary characteristics are modelled with the aid of a hypergraph representation. The underlying reasoning concept of a possibilistic focusing system is outlined and compared with two alternative approaches in this field.

This work has partially been funded by CEC-ESPRIT III Basic Research Project 6156 (DRUMS II)

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References

  1. S. Benferhat, D. Dubois, J. Lang, and H. Prade. Hypothetical reasoning in possibilistic logic: Basic notions and implementation issues. In P.Z. Wang and K.F. Loe, editors, Advances in Fuzzy Systems — Vol. 1. World Scientific Publisher, Singapore, 1992.

    Google Scholar 

  2. D. Dubois and H. Prade. A fuzzy relation-based extension of Reggia's relational model for diagnosis handling uncertain and incomplete information. In Proc. 9th Conf. on Uncertainty in Artificial Intelligence, Washington, pages 106–113, 1993.

    Google Scholar 

  3. J. Gebhardt and R. Kruse. A new approach to semantic aspects of possibilistic reasoning. In M. Clarke, R. Kruse, and S. Moral, editors, Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Lecture Notes in Computer Science, 747, pages 151–160. Springer, Berlin, 1993.

    Google Scholar 

  4. J. Gebhardt and R. Kruse. Learning possibilistic networks from data. In Proc. 5th Int. Workshop on Artificial Intelligence and Stati stics, pages 233–244, Fort Lauderdale, 1995.

    Google Scholar 

  5. J. de Kleer and B.C. Williams. Diagnosing multiple faults. Artificial Intelligence, 32:97–130, 1987.

    Google Scholar 

  6. R. Kruse, J. Gebhardt, and F. Klawonn. Foundations of Fuzzy Systems. Wiley, Chichester, 1994.

    Google Scholar 

  7. H.T. Nguyen. On random sets and belief functions. J. of Mathematical Analysis and Applications, 65:531–542, 1978.

    Google Scholar 

  8. J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, New York, 1988.

    Google Scholar 

  9. Y. Peng and J.A. Reggia. Diagnostic problem solving with causal chaining. Int. J. of Intelligent Systems, 2:265–302, 1987.

    Google Scholar 

  10. Y. Peng and J.A. Reggia. Abductive Inference Models for Diagnostic Problem-Solving. Springer, New York, 1990.

    Google Scholar 

  11. D. Poole. Probabilistic horn anduction and bayesian networks. Artificial Intelligence, 64:81–129, 1993.

    Google Scholar 

  12. J.A. Reggia, D.S. Nau, P.Y. Wang, and H. Peng. A formal model of diagnostic inference. Information Sciences, 37:227–285, 1985.

    Google Scholar 

  13. R. Reiter. Nonmonotonic reasoning. Annual Review of Computer Science, 2:147–186, 1987.

    Google Scholar 

  14. E. Sanchez. Solutions in composite fuzzy relation equations: Application to medical diagnosis in Brouwerian logic. In M.M. Gupta, G.N. Saridis, and B.R. Gaines, editors, Fuzzy Automata and Decision Processes, pages 221–234. North Holland, Amsterdam, 1977.

    Google Scholar 

  15. E. Sanchez. Inverses of fuzzy relations, application to possibility distributions and medical diagnosis. Fuzzy Sets and Systems, 2:75–86, 1979.

    Google Scholar 

  16. Y. Tsukamoto and T. Terano. Failure diagnosis by using fuzzy logic. In Proc. IEEE Conf. on Decision and Control, New Orleans, pages 1390–1395, 1977.

    Google Scholar 

  17. L.A. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1:3–28, 1978.

    Google Scholar 

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Bernadette Bouchon-Meunier Ronald R. Yager Lotfi A. Zadeh

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© 1995 Springer-Verlag Berlin Heidelberg

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Gebhardt, J., Kruse, R. (1995). A numerical framework for possibilistic abduction. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Advances in Intelligent Computing — IPMU '94. IPMU 1994. Lecture Notes in Computer Science, vol 945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035961

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  • DOI: https://doi.org/10.1007/BFb0035961

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60116-6

  • Online ISBN: 978-3-540-49443-0

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