Skip to main content
SpringerLink
Log in

Possibility-Probability Relation in Medical Models

  • Conference paper
Medical Data Analysis (ISMDA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2868))

Included in the following conference series:

  • 503 Accesses

Abstract

Medical models based on possibility theory are usually much simpler than those based on probability theory, but they lack foundations. The most foundational question is: How to obtain a possibility distribution for a modeling process? As one of the solutions, a simple framework is proposed built on the conjecture that a probability distribution for an uncertain process can be predicted by the process’s possibility distribution. The case of the perfect prediction and the case of possibility and probability distributions related less than perfect (modeling ”ideal body weight”) are considered in this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abbod, M., von Keyserlingk, D., Linkens, D., Mahfouf, M.: Survey of utilization of fuzzy technology in Medicine and Healthcare. Fuzzy Sets and Systems 120, 331–349 (2001)

    Article  MathSciNet  Google Scholar 

  2. Halpern, J., Pucella, R.: Logic for Reasoning about Upper Probabilities. Articial Intelligence Research 17, 57–81 (2002)

    MATH  MathSciNet  Google Scholar 

  3. Dubois, D., Prade, H.: An introduction to possibilistic and fuzzy logics. In: Smets, P., Mamdani, A., Dubois, D., Prade, H. (eds.) Non-Standard Logics for Automated Reasoning, pp. 287–315. Academic Press, London (1988)

    Google Scholar 

  4. Lapointe, S., Bobée, B.: Revision of possibility distributions: A Bayesian inference patern. Fuzzy sets and systems 116, 119–140 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Zadeh, L.: Fuzzy sets as a basis for theory of possibility. Fuzzy sets and systems 1, 3–28 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  6. Zadeh, L.: PRUF - a measuring representation language for natural languages. Internal J. Man-Machine Studies 10, 395–460 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  7. Zadeh, L.: Possibility theory and soft data analysis. In: Cobb, L., Thrall, R. (eds.) Mathematical Frontiers of the Social and Policy Sciences, pp. 69–129. Westview Press, Boulder CO (1981)

    Google Scholar 

  8. Klir, G.: On fuzzy-set interpretation of possibility theory. Fuzzy sets and systems 108, 263–273 (2000)

    Article  MathSciNet  Google Scholar 

  9. Walley, P.: Measures of uncertainty in expert systems. Artificial Intelligence 83, 1–58 (1996)

    Article  MathSciNet  Google Scholar 

  10. de Cooman, G.: Possibility Theory I: The measure- and integral-theoretic groundwork. Internat. J. General Systems 25, 291–323 (1997)

    Article  MATH  Google Scholar 

  11. Janssen, H., de Cooman, G., Kerre, E.: A Daniel-Kolmogorov theorem for supre-mum preserving upper probabilities. Fuzzy sets and systems 102, 429–444 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. Nguyen, H.: Fuzzy sets and probability. Fuzzy sets and systems 90, 129–132 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Bolotin, A.: A Generalized Uncertainty Function and Fuzzy Modeling. In: Crespo, J.L., Maojo, V., Martin, F. (eds.) ISMDA 2001. LNCS, vol. 2199, pp. 75–80. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Mehra, J., Rechenberg, H.: The Historical Development of Quantum Theory. Springer, Heidelberg (2001)

    MATH  Google Scholar 

  15. Strap, H.: The Copenhagen Interpretation and the Nature of Space-Time. American Journal of Physics 40, 1098 (1972)

    Article  Google Scholar 

  16. Heisenberg, W.: Physics and Philosophy. Harper Torch Books, New York (1958)

    Google Scholar 

  17. von Neumann, J.: The Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1955)

    MATH  Google Scholar 

  18. Bell, J.: Bertlmann’s socks and the nature of reality. J. Phys. C 2, 41–62 (1981)

    Google Scholar 

  19. Dalibard, J., Basdevant, J.-L.: The Quantum Mechanics Solver: How to Apply Quantum Theory to Modern Physics (Advanced Texts in Physics). Springer Verlag, Heidelberg (2000)

    Google Scholar 

  20. Grauel, A., Ludwig, L.: Construction of differentiable membership functions. Fuzzy sets and systems 101, 219–225 (1999)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Epidemiology and Health Sciences Evaluation, Ben-Gurion University of the Negev, P.O. Box 653, Beersheba, 84105, Israel

    A. Bolotin

Authors
  1. A. Bolotin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Computer Vision and applied Computer Sciences, IBaI, Germany

    Petra Perner

  2. Institute of Informatics, Johann Wolfgang Goethe-Universität, 60054, Frankfurt a.M., Germany

    Rüdiger Brause

  3. Institut für Biochemie, Charité, Campus Mitte, Monbijoustr. 2, 10117, Berlin, Germany

    Hermann-Georg Holzhütter

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bolotin, A. (2003). Possibility-Probability Relation in Medical Models. In: Perner, P., Brause, R., Holzhütter, HG. (eds) Medical Data Analysis. ISMDA 2003. Lecture Notes in Computer Science, vol 2868. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39619-2_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-39619-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20282-0

  • Online ISBN: 978-3-540-39619-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation