Advertisement

Conditional Events and Fuzzy Conditional Events Viewed from a Product Probability Space Perspective

  • I. R. Goodman
Part of the Theory and Decision Library book series (TDLD, volume 16)

Abstract

This paper first provides a brief review of the product space approach to conditional event algebra and the one-point random set coverage function representation of fuzzy sets followed by a natural extension to a fuzzy set structure.

Keywords

Membership Function Fuzzy Logic Conditional Event Logical Combination Point Coverage 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Goodman, I.R., Nguyen, H.T. & Walker, E.A., Conditional Inference and Logic for Intelligent Systems: A Theory of Measure-Free Conditioning, North-Holland, Amsterdam, 1991.Google Scholar
  2. 2.
    Goodman, I.R., “Toward a comprehensive theory of linguistic and probabilistic evidence:two new approaches to conditional event algebra”, IEEE Trans. Systems, Man & Cybernetics (special issue on conditionals) 24(12), Dec., 1994, 1685–1698.Google Scholar
  3. 3.
    Van Fraasen, B., “Probabilities of Conditionals”, in book Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, 1(W.L. Harper & C.A. Hooker, eds.), D. Reidel, Dordrecht, Netherlands, 1976, pp. 261–308.Google Scholar
  4. 4.
    Calabrese, P.G., “A theory of conditional information with applications”, IEEE Transactions on Systems, Man & Cybernetics (special issue on conditionals), 24(12), Dec., 1994, 1676–1684.MathSciNetGoogle Scholar
  5. 5.
    B. Schweizer, B. & Sklar, A., Probabilistic Metric Spaces, North-Holland, New York, 1983.zbMATHGoogle Scholar
  6. 6.
    Goodman, I.R. & Nguyen, H.T., Uncertainty Models for Knowledge-Based Systems, North-Holland, New York, 1985.zbMATHGoogle Scholar
  7. 7.
    Goodman, I.R., “A new characterization of fuzzy logic operators producing homomorphic-like relations with one-point coverages of random sets”, in book Advances in Fuzzy Theory & Technology, 2 (P.P. Wang, ed.), Bookwright Press, Durham, NC., pp. 133–159.Google Scholar
  8. 8.
    Goodman, I.R., “Some new results concerning random sets and fuzzy sets”, Information Sciences, 34, Nov., 1984, 93–113.CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Goodman, I.R., “Algebraic and probabilistic bases for fuzzy sets and the development of fuzzy conditioning”, in book Conditional Logic in Expert Systems (I.R. Goodman, M.M. Gupta, H.T. Nguyen & G.S. Rogers, eds.), North-Holland, Amsterdam, Netherlands, 1991, pp. 1–69.Google Scholar
  10. 10.
    Goodman, I.R., “Applications of product space algebra of conditional events and one- point random set representations of fuzzy sets to the development of conditional fuzzy sets”, Fuzzy Sets & Systems (special issue, D. Ralescu, ed.), to appear.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • I. R. Goodman
    • 1
  1. 1.NCCOSC RDTE DIV (NRaD)San DiegoUSA

Personalised recommendations