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Qualitative versus quantitative interpretation of the mathematical theory of evidence

  • Communications Session 5A Approximate Reasoning
  • Conference paper
  • First Online:
Foundations of Intelligent Systems (ISMIS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1325))

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Abstract

The paper presents a novel view of the Dempster-Shafer belief function as a measure of diversity in relational data bases. The Dempster rule of evidence combination corresponds to the join operator of the relational database theory. This rough-set based interpretation is qualitative in nature and can represent a number of belief function operators.

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References

  1. Beeri C., Fagin R., Maier D., Yannakakis Y.: On the desirability of acyclic database schemes, Journal of the Association for Computing Machinery, vol. 30, no 3, 1983, 479–513.

    Google Scholar 

  2. Delobel C.: Normalization and hierarchical dependencies in the relational data model, ACM Transactions on Database Systems, vol. 3, no 3, 1978, 201–222.

    Google Scholar 

  3. Dempster A.P.: Upper and lower probabilities induced by a multi-valued mapping. Ann. Math. Stat.. 38 (1967), 325–339.

    Google Scholar 

  4. Fagin R., Halpern J.Y.: Uncertainty, belief, and probability. Comput. Intell. 7 (1991), 160–173.

    Google Scholar 

  5. Klopotek M.A.: Interpretation of belief function in Dempster-Shafer Theory Foundations of Computing & Decision Sciences, Vol. 20 No 4, 1995, pp.287–306

    Google Scholar 

  6. Kyburg Jr H.E.: Bayesian and non-Bayesian evidential updating. Artificial Intelligence 31 (1987), 271–293.

    Google Scholar 

  7. Pearl J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Influence. Morgan and Kaufmann, 1988

    Google Scholar 

  8. Provan G.M.: A logic-based analysis of Dempster-Shafer Theory, International Journal of Approximate Reasoning 4 (1990), 451–495.

    Google Scholar 

  9. Ras, Z.W.: Query processing in distributed information systems, Fundamenta Informaticae Journal, Special Issue on Logics for Artificial Intelligence, IOS Press, Vol. XV, No. 3/4, 1991, 381–397

    Google Scholar 

  10. Ruspini E.H.: The logical foundation of evidential reasoning, Tech. Note 408, SRI International, Menlo Park, Calif. USA, 1986.

    Google Scholar 

  11. Ruspini E.H.: The logical foundation of evidential reasoning, Tech. Note 408, SRI International, Menlo Park, Calif. USA, 1986.

    Google Scholar 

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

    Google Scholar 

  13. Shafer G.: Belief functions: An introduction.In: Shafer G., Pearl J.,eds, Readings in Uncertain Reasoning. Morgan Kaufmann Pub.Inc., San Mateo CA, (1990), 473–482.

    Google Scholar 

  14. Shafer G., Srivastava R.: The Bayesian and Belief-Function Formalisms. A General Prospective for Auditing. In: Shafer G., Pearl J.,eds, Readings in Uncertain Reasoning. Morgan Kaufmann Pub.Inc., San Mateo CA, (1990), 482–521.

    Google Scholar 

  15. Shafer G.: Perspectives on the theory and practice of belief functions. International Journal of Approximate Reasoning 4 (1990), 323–362.

    Google Scholar 

  16. Shenoy P.P.: Conditional independence in valuation based systems. International Journal of Approximate Reasoning 109(1994)

    Google Scholar 

  17. Skowron A., Grzymala-Busse J.W.: From rough set theory to evidence theory. In:Yager R.R., Kasprzyk J. and Fedrizzi M., eds, Advances in the Dempster-Shafer Theory of Evidence. J. Wiley, New York (1994), 193–236.

    Google Scholar 

  18. Smets Ph.: Resolving misunderstandings about belief functions. International Journal of Approximate Reasoning 6 (1992), 321–344.

    Google Scholar 

  19. Wasserman L.: Comments on Shafer's “Perspectives on the theory and practice of belief functions”. International Journal of Approximate Reasoning 6 (1992),367–375.

    Google Scholar 

  20. Vang A.: SQL and Relational Databases. Microtrend Books, Slawson Communications Inc., 1991

    Google Scholar 

  21. Wierzchoń S.T.: On plausible reasoning, in: M.M.Gupta, T.Yamakawa eds.: Fuzzy Logic in Knowledge Based Systems, Decision and Control, North-Holland Amsterdam, 1988, 133–152.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Computer Science, Polish Academy of Sciences, Warszawa, Poland

    M. A. Klopotek & S. T. Wierzchoń

Authors
  1. M. A. Klopotek
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  2. S. T. Wierzchoń
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Zbigniew W. Raś Andrzej Skowron

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© 1997 Springer-Verlag Berlin Heidelberg

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Klopotek, M.A., Wierzchoń, S.T. (1997). Qualitative versus quantitative interpretation of the mathematical theory of evidence. In: Raś, Z.W., Skowron, A. (eds) Foundations of Intelligent Systems. ISMIS 1997. Lecture Notes in Computer Science, vol 1325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63614-5_38

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  • DOI: https://doi.org/10.1007/3-540-63614-5_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63614-4

  • Online ISBN: 978-3-540-69612-4

  • eBook Packages: Springer Book Archive

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