Skip to main content

Imperfect Information: Imprecision and Uncertainty

  • Chapter
Uncertainty Management in Information Systems

Abstract

Imperfection, be it imprecision or uncertainty, pervades real-world scenarios and must therefore be incorporated into every information system that attempts to provide a complete and accurate model of the real world. Yet, this is hardly achieved in today’s information systems. A major reason might be the inherent difficulty of understanding the various aspects of imprecision and uncertainty.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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. M. Black. Vagueness: an exercise in logical analysis. Philosophy of Science, 4: 427–455, 1937.

    Article  Google Scholar 

  2. D. G. Bobrow. Special issue on non-monotonic logics. Artificial Intelligence, 13, 1980.

    Google Scholar 

  3. R. Carnap. Logical Foundations of Probability. Chicago University Press, 1950.

    Google Scholar 

  4. D. A. Clark. Verbal uncertainty expressions: a review of two decades of research. Current Psychology: Research and Reviews, 9: 203–235, 1990.

    Article  Google Scholar 

  5. M. R. B. Clarke, C. Froidevaux, E. Gregoire, and Ph. Smets. Uncertainty, conditional and non-monotonicity: Positions and debates in non-standard logics. Journal of Applied Non-Classical Logics, 1: 103–310, 1991.

    MathSciNet  Google Scholar 

  6. R. T. Cox. Probability, frequency and reasonable expectation. Amer. J. Phys., 14: 1–13, 1946.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Degroot. Optimal Statistical Decisions. McGraw Hill, New York, 1970.

    Google Scholar 

  8. A. P. Dempster. Upper and lower probabilities induced by a multiplevalued mapping. Ann. Math. Statistics., 38: 325–339, 1967.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. P. Dempster. A generalization of Bayesian inference. Journal Royal Statistical Society, B.30: 205–247, 1968.

    MathSciNet  Google Scholar 

  10. D. Dubois, P. Garbolino, H. E. Kyburg, H. Prade, and Ph. Smets. Quantified uncertainty. Journal of Applied Non-Classical Logics, 1: 105–197, 1991.

    MathSciNet  MATH  Google Scholar 

  11. D. Dubois and H. Prade. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.

    MATH  Google Scholar 

  12. D. Dubois and H. Prade. A review of fuzzy sets aggregation connectives. Information Sciences, 36: 85–121, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. Dubois and H. Prade. Theory of Possibility. Plenum, London, 1988.

    Book  MATH  Google Scholar 

  14. J. Earman. Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory. MIT Press, Cambridge, MA, 1992.

    Google Scholar 

  15. R. Fagin and J. Halpern. A new approach to updating beliefs. In L. N. Kanal P. P. Bonissone, M. Henrion and J. F. Lemmer, editors, Uncertainty in Artificial Intelligence 6, pages 347-374. North Holland, Amsterdam, 1991.

    Google Scholar 

  16. B. De Finetti. Theory of Probability Vol. 1 and Vol. 2. Wiley, London, 1974.

    Google Scholar 

  17. M. L. Ginsberg. Readings in Nonmonotonic Reasoning. Morgan Kaufmann, San Mateo, CA, 1988.

    Google Scholar 

  18. I. J. Good. Probability and the Weighting of Evidence. Hafner, 1950.

    Google Scholar 

  19. I. J. Good. Good Thinking: the Foundations of Probability and Its Applications. University of Minnesota Press, Minneapolis, 1983.

    MATH  Google Scholar 

  20. I. Hacking. Logic of Statistical Inference. Cambridge University Press, 1965.

    Google Scholar 

  21. I. Hacking. The Emergence of Probability. Cambridge University Press, 1975.

    Google Scholar 

  22. J. Y. Jaffray. Bayesian updating and belief functions. IEEE Trans. SMC, 22: 1144–1152, 1992.

    MathSciNet  MATH  Google Scholar 

  23. R. Jeffrey. Conditioning, kinematics and exchangeability. In B. Skyrms and W. L. Harper, editors, Causation, Chance and Credence Vol. 1, pages 221–255. Reidel, Dordrecht, 1988.

    Google Scholar 

  24. J. M. Keynes. A Treatise on Probability. Harper and Row, New York, 1962.

    MATH  Google Scholar 

  25. P. Krause and D. Clark. Representing Uncertain Knowledge. An AI Approach. Intellect, Oxford, 1993.

    Book  Google Scholar 

  26. I. Levi. Decisions and Revisions: Philosophical Essays on Knowledge and Value. Cambridge University Press, Cambridge, 1984.

    Book  Google Scholar 

  27. W. Lukaszewicz. Nonmonotonic Reasoning. Ellis Horwood, Chichester, 1990.

    Google Scholar 

  28. R. Von Mises. Probability, Statistics and Truth (2nd Edition). Allen and Unwin, London, 1957.

    Google Scholar 

  29. K. R. Popper. The Logic of Scientific Discovery. Basic Books, New York, 1959.

    MATH  Google Scholar 

  30. H. Reichenbach. The Theory of Probability. University of California Press, Berkeley, 1949.

    MATH  Google Scholar 

  31. R. Reiter. Nonmonotonic reasoning. Annual Review of Computer Science, pages 147-186, 1987.

    Google Scholar 

  32. L. J. Savage. Foundations of Statistics. Wiley, New York, 1954.

    MATH  Google Scholar 

  33. G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, Princeton, 1976.

    MATH  Google Scholar 

  34. Ph. Smets. Probability of a fuzzy event: an axiomatic approach. International Journal of Fuzzy Sets and Systems, 7: 153–164, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  35. Ph. Smets. Probability of a fuzzy event. In M. G. Singh, editor, Systems and Control Encyclopedia, pages 1802–1805. Pergamon, Oxford, 1985.

    Google Scholar 

  36. Ph. Smets. Upper and lower probability functions versus belief functions. In Proceedings of ISFK International Symposium on Fuzzy Systems and Knowledge Engineering (Guangzhou, China, July 10–July 16), pages 17-21. ISFK, 1987.

    Google Scholar 

  37. Ph. Smets. Belief functions. In D. Dubois Ph. Smets, A. Mamdani and H. Prade, editors, Nonstandard Logics for Automated Reasoning, pages 253–286. Academic Press, London, 1988.

    Google Scholar 

  38. Ph. Smets. Constructing the pignistic probability function in a context of uncertainty. In L. N. Kanal M. Henrion, R. D. Shachter and J. F. Lemmer, editors, Uncertainty in Artificial Intelligence 5, pages 29–40. North Holland, Amsterdam, 1990.

    Google Scholar 

  39. Ph. Smets. Implication and modus ponens in fuzzy logic. In H. T. Nguyen I. R. Goodman, M. M. Gupta and G. S. Rogers, editors, Conditional Logic in Expert Systems, pages 235–268. Elsevier, Amsterdam, 1991.

    Google Scholar 

  40. Ph. Smets and R. Kennes. The transferable belief model. Artificial Intelligence, 66: 191–234, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  41. Ph. Smets and P. Magrez. The measure of the degree of truth and of the grade of membership. International Journal of Fuzzy Sets and Systems, 25: 67–72, 1988.

    Article  MathSciNet  Google Scholar 

  42. C. A. B. Smith. Consistency in statistical inference and decision. Journal of the Royal Statistical Society, B23: 1–37, 1961.

    Google Scholar 

  43. C. A. B. Smith. Personal probability and statistical analysis. Journal of the Royal Statistical Society, A128: 469–499, 1965.

    Google Scholar 

  44. M. Smithson. Ignorance and Uncertainty: Emerging Paradigms. Springer-Verlag, New York, 1989.

    Book  Google Scholar 

  45. M. Sugeno. Fuzzy measures and fuzzy integrals: a survey. In G. N. Saridis M. M. Gupta and B. R. Gaines, editors, Fuzzy Automata and Decision Processes, pages 89-102. North Holland, Amsterdam, 1977.

    Google Scholar 

  46. P. Teller. Conditionalization and observation. Synthesis, 26: 218–258, 1973.

    Article  MATH  Google Scholar 

  47. P. Teller. Conditionalization, observation and change of preference. In W. Harper and C. A. Hooker, editors, Foundations of Probability Theory, Statistical Inference and Statistical Theory of Science, pages 205–259. Reidel, Doordrecht, 1976.

    Chapter  Google Scholar 

  48. P. Walley. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London, 1991.

    MATH  Google Scholar 

  49. R. Yager. Connectives and quantifiers in fuzzy sets. International Journal Fuzzy Sets and Systems, 40: 39–76, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  50. L. Zadeh. Fuzzy sets. Information and Control, 8: 338–353, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  51. L. Zadeh. Probability measures of fuzzy events. J. Math. Anal. Appl, 23: 421–427, 1968.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this chapter

Cite this chapter

Smets, P. (1997). Imperfect Information: Imprecision and Uncertainty. In: Motro, A., Smets, P. (eds) Uncertainty Management in Information Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6245-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-6245-0_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7865-5

  • Online ISBN: 978-1-4615-6245-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics