Advertisement

Interval approaches for uncertain reasoning

  • Y. Y. Yao
  • S. K. M. Wong
Communications Session 5A Approximate Reasoning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1325)

Abstract

This paper presents a framework for reasoning using intervals. Two interpretations of intervals are examined, one treats intervals as bounds of a truth evaluation function, and the other treats end points of intervals as two truth evaluation functions. They lead to two different reasoning approaches, one is based on interval computations, and the other is based on interval structures. A number of interval based reasoning methods are reviewed and compared within the proposed framework.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Brink, Power structures, Algebra Universalis, 30, 177–216, 1993.Google Scholar
  2. 2.
    P.P. Bonissone, Summarizing and propagating uncertain information with triangular norms, International Journal of Approximate Reasoning, 1, 71–101, 1987.Google Scholar
  3. 3.
    A. Bundy, Incidence calculus: a mechanism for probabilistic reasoning, Journal of Automated Reasoning, 1, 263–283, 1985.Google Scholar
  4. 4.
    D. Dubois, and P. Prade, Possibility Theory: an Approach to Computerized Processing of Uncertainty, Plenum Press, New York, 1988.Google Scholar
  5. 5.
    R. Fagin, and J.Y. Halpern, Uncertainty, belief, and probability, Computational Intelligence, 7, 160–173, 1991.Google Scholar
  6. 6.
    J.Y. Halpern, and R. Fagin, Two views of belief: belief as generalized probability and belief as evidence, Artificial Intelligence, 54: 275–317, 1992.Google Scholar
  7. 7.
    G.J. Klir, and B. Yuan, Fuzzy Sets and Fuzzy Logic. Theory and Applications, Prentice Hall, New Jersey, 1995.Google Scholar
  8. 8.
    R.E. Moore, Interval Analysis, Englewood Cliffs, New Jersey, Prentice-Hall, 1966.Google Scholar
  9. 9.
    C.V. Negoiţa, and D.A. Ralescu, Applications of Fuzzy Sets to Systems Analysis, Basel, Birkhäuser Verlag, 1975.Google Scholar
  10. 10.
    Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11, 341–356, 1982.Google Scholar
  11. 11.
    J.R. Quinlan, Inferno: a cautious approach to uncertain inference, The Computer Journal, 26, 255–269, 1983.Google Scholar
  12. 12.
    G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, Princeton, 1976.Google Scholar
  13. 13.
    P. Smets, Resolving misunderstandings about belief functions, International Journal of Approximate Reasoning, 6, 21–344.Google Scholar
  14. 14.
    S.K.M. Wong, L.S. Wang, and Y.Y. Yao, On modeling uncertainty with interval structures, Computational Intelligence, 11, 406–426, 1995.Google Scholar
  15. 15.
    Y.Y. Yao, Interval-set algebra for qualitative knowledge representation, Proceedings of the Fifth International Conference on Computing and Information, 370–374, 1993.Google Scholar
  16. 16.
    Y.Y. Yao, A comparison of two interval-valued probabilistic reasoning methods, Proceedings of the 6th International Conference on Computing and Information, May 26–28, 1994, Peterborough, Ontario, Canada. Special issue of Journal of Computing and Information, 1, 1090–1105 (paper number D6), 1995.Google Scholar
  17. 17.
    Y.Y. Yao, and X. Li, Comparison of rough-set and interval-set models for uncertain reasoning, Fundamenta Informaticae, 27, 289–298, 1996.Google Scholar
  18. 18.
    Y.Y. Yao, and N. Noroozi, A unified framework for set-based computations, Proceedings of the 3rd International Workshop on Rough Sets and Soft Computing, Lin, T.Y. (Ed.), San Jose State University, 236–243, 1994.Google Scholar
  19. 19.
    Y.Y. Yao, and J. Wang, Interval based uncertain reasoning using fuzzy and rough sets, Advances in Machine Intelligence & Soft-Computing, Volume IV, Wang, P.P. (Ed.), Department of Electrical Engineering, Duke University, Durham, North Carolina, USA, 196–215, 1997Google Scholar
  20. 20.
    Y.Y. Yao, S.K.M. Wong, and L.S. Wang, A non-numeric approach to uncertain reasoning, International Journal of General Systems, 23, 343–359, 1995.Google Scholar
  21. 21.
    L.A. Zadeh, Fuzzy sets, Information & Control, 8, 338–353, 1965.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Y. Y. Yao
    • 1
  • S. K. M. Wong
    • 2
  1. 1.Department of Computer ScienceLakehead UniversityOntario
  2. 2.Department of Computer ScienceUniversity of ReginaSaskatchewanS4S 0A2

Personalised recommendations