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Annals of Operations Research

, Volume 32, Issue 1, pp 51–66 | Cite as

Additive functions and their application to uncertain information

  • Thomas Kämpke
Article

Abstract

For additive functions over ordered sets, a minimum representation is given in case the ordered set has a particular deviation property. Additive functions are known to be special supermodular functions on power sets and in probability calculus, they are related to, for example, capacities and distribution functions of random sets. Their capability to encode vague information is stressed.

Keywords

Distribution Function Additive Function Minimum Representation Deviation Property Uncertain Information 
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]
    M. Aigner,Kombinatorik I (Springer, Berlin, 1975).Google Scholar
  2. [2]
    G. Birkhoff,Lattice Theory (American Mathematical Society, Providence, 1940; Reprint of 3rd ed., 1984).Google Scholar
  3. [3]
    R. K. Bhatnagar and L. N. Kanal, Handling uncertain information: A review of numeric and non-numeric methods, in:Uncertainty in Artificial Intelligence, Vol. 4, ed. L. N. Kanal and J. F. Lemmer (North-Holland, Amsterdam, 1988).Google Scholar
  4. [4]
    P. J. Huber and V. Strassen, Minimax tests and the Neyman-Pearson lemma for capacities, Ann. Statist. 1(1973)251–263.Google Scholar
  5. [5]
    E. L. Lawler,Combinatorial Optimization: Networks and Matroids (Holt, Rinehart and Winston, New York, 1976).Google Scholar
  6. [6]
    L. Lovász, Supermodular functions and convexity, in:Mathematical Programming, ed. A. Bachem, M. Grötschel and B. Korte (Springer, Berlin, 1983), pp. 235–257.Google Scholar
  7. [7]
    H. T. Nguyen, On random sets and belief functions, J. Math. Anal. Appl. 65(1978)531–542.Google Scholar
  8. [8]
    G.-C. Rota, On the foundation of combinatorial theory I. Theory of Möbius functions, Z. für Wahrscheinlichkeitstheorie 2(1964)340–368.Google Scholar
  9. [9]
    G. Shafer,A Mathematical Theory of Evidence (Princeton University Press, Princeton, 1976).Google Scholar
  10. [10]
    D. Stoyan, W. S. Kendall and J. Mecke,Stochastic Geometry and its Applications (Wiley, Chichester, 1987).Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1991

Authors and Affiliations

  • Thomas Kämpke
    • 1
  1. 1.Forschungsinstitut für anwendungsorientierte Wissensverarbeitung (FAW)University of UlmUlmGermany

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