Abstract

A comprehensive model for evaluating specificity of fuzzy sets is presented. It is designed in terms of possibility values, independent of the domain of discourse. For a discrete distribution π = (p1p2 ≥ …) two measures are defined exponential logarithmic I(π) =∑(pi - Pi+1)log i Measure Sp(π) is derived from a few intuitively plausible properties of specificity; measure I(π) is dual to nonspecificity in Dempster-Shafer theory.

The resulting model has a natural OWA structure, which follows necessarily from the basic assumptions. This leads to an inverse problem, one of developing, within the general OWA framework, the features successfully employed in specificity and uncertainty models. We suggest some directions in the concluding section.

Keywords

Possibility Distribution Possibility Theory Ordered Weight Average Infinite Case Informal Specificity 
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.

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References

  1. [1]
    D. Dubois, H. Prade. Properties of measures of information in evidence and possibility theories. Fuzzy Sets and Systems 24(1988), 2:161–182.MathSciNetCrossRefGoogle Scholar
  2. [2]
    D. Dubois, H. Prade. Possibility Theory. Plenum Press, New York 1988.MATHCrossRefGoogle Scholar
  3. [3]
    G. Hardy, J. Littlewood, G. Polya. Inequalities, 2nd ed. Cambridge University Press, Cambridge, 1964.Google Scholar
  4. [4]
    M. Higashi. G. Klir. On the notion of distance representing information closeness, Int. J. General Systems, 9(1983), 2:103–115.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    M. Higashi, G. Klir. Measures of uncertainty and information based on possibility distributions. Int. J. General Systems, 9(1982), 1:43–58.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    A. Ramer. Ordered continuous means and information. Chapter in this book.Google Scholar
  7. [7]
    A. Ramer. Combinatorial interpretation of uncertainty and conditioning. Chapter in: Learning and Reasoning with Complex Representations, ed: G. Antoniou, Lecture Notes in Computer Science, Springer-Verlag, New York 1997 (to appear).Google Scholar
  8. [8]
    A. Ramer. Uncertainty generating functions, Chapter in: Foundations and Applications of Possibility Theory, ed: W. Chiang, J. Lee, World Scientific, Singapore, 1996.Google Scholar
  9. [9]
    A. Ramer. Structure of possibilistic information metrics and distances. Part 1: Properties. Int. J. General Systems 17(1990), 1:21–32. Part 2: Characterization, ibid 18(1990), 1:1-10.MATHCrossRefGoogle Scholar
  10. [10]
    A. Ramer. Conditional possibility measures, Cybernetics and Systems, 20(1989), 233–247. Reprinted in: Readings in Fuzzy Sets for Intelligent Systems, ed: D. Dubois, H. Prade, R. Yager. Morgan Kaufmann, San Mateo, CA 1993.Google Scholar
  11. [11]
    A. Ramer. Uniqueness of information measure in the theory of evidence. Fuzzy Sets and Systems, 24(1987), 2:183–196.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    A. Ramer, L. Lander. Classification of possibilistic measures of uncertainty and information. Fuzzy Sets and Systems, 24(1987), 2:221–230.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    A. Ramer, C. Padet. Possibility, probability, and specificity-decisions in a fuzzy world, IFSICC’93 — Int. Fuzzy Systems and Intelligent Control Conf., Louisville, KY, March 1993.Google Scholar
  14. [14]
    A. Ramer, R. Yager. Specificity and information in fuzzy systems, FUZZ-IEEE’ 92, San Diego, CA, March 1992.Google Scholar
  15. [15]
    R. Yager Entropy and specificity in a mathematical theory of evidence. Int. J. General Systems 9(1983).Google Scholar
  16. [16]
    R. Yager. On measuring specibcity. Tech. Rep., Iona College, New Rochelle, NY 1990.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Arthur Ramer
    • 1
  1. 1.Knowledge Systems Group, Computer ScienceUniversity of New South WalesSydneyAustralia

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