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The α-junctions: Combination operators applicable to belief functions

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Qualitative and Quantitative Practical Reasoning (FAPR 1997, ECSQARU 1997)

Abstract

Derivation through axiomatic arguments of the operators that represent associative, commutative and non interactive combinations within belief function theory. The derived operators generalize the conjunction, disjunction and exclusive disjunction cases. The operators are characterized by one parameter.

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Bibliography

  • DUBOIS D. and PRADE H. (1986) A set theoretical view of belief functions. Int. J. Gen. Systems, 12:193–226.

    Google Scholar 

  • GEBHARDT J. and KRUSE R. (1993) The Context Model: An Integrating View of Vagueness and Uncertainty, Int. J. of Approximate Reasoning 9, 283–314.

    Google Scholar 

  • KENNES R. and SMETS Ph. (1990) Computational Aspects of the Möbius Transform. in Bonissone P.P., Henrion M., Kanal L.N. and Lemmer J.F. eds., Uncertainty in Artificial Intelligence 6. North Holland, Amsteram, 1991, 401–416.

    Google Scholar 

  • KENNES R. (1992) Computational aspects of the Moebius transform of a graph. IEEE-SMC, 22: 201–223.

    Google Scholar 

  • KLAWONN F. and SMETS Ph. (1992) The dynammic of belief in the transferable belief model and specialization-generalization matrices. in Dubois D., Wellman M.P., D'Ambrosio B. and Smets Ph. Uncertainty in AI 92. Morgan Kaufmann, San Mateo, Ca, USA, 1992, pg. 130–137.

    Google Scholar 

  • SHAFER G. (1976) A mathematical theory of evidence. Princeton Univ. Press. Princeton, NJ.

    Google Scholar 

  • SMETS Ph. (1983) Information Content of an Evidence. Int. J. Man Machine Studies, 19: 33–43.

    Google Scholar 

  • SMETS Ph. (1990) The combination of evidence in the transferable belief model. IEEE Pattern analysis and Machine Intelligence, 12:447–458.

    Google Scholar 

  • SMETS Ph. (1992) The concept of distinct evidence. IPMU 92 Proceedings.pg. 789–794.

    Google Scholar 

  • SMETS Ph. (1993a) Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. Int. J. Approximate Reasoning 9:1–35.

    Google Scholar 

  • SMETS Ph. (1993b) An axiomatic justifiaction for the use of belief function to quantify beliefs. IJCAI'93 (Inter. Joint Conf. on AI), Chambery. pg. 598–603.

    Google Scholar 

  • SMETS Ph. (1997) Imperfect information: imprecision — uncertainty. In Motro A. and Smets Ph. eds.Uncertainty Management in Information Systems. Kluwer, Boston, pg. 225–254.

    Google Scholar 

  • SMETS Ph. and KENNES R. (1994) The transferable belief model. Artificial Intelligence 66:191–234.

    Google Scholar 

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Dov M. Gabbay Rudolf Kruse Andreas Nonnengart Hans Jürgen Ohlbach

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© 1997 Springer-Verlag Berlin Heidelberg

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Smets, P. (1997). The α-junctions: Combination operators applicable to belief functions. In: Gabbay, D.M., Kruse, R., Nonnengart, A., Ohlbach, H.J. (eds) Qualitative and Quantitative Practical Reasoning. FAPR ECSQARU 1997 1997. Lecture Notes in Computer Science, vol 1244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035618

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  • DOI: https://doi.org/10.1007/BFb0035618

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63095-1

  • Online ISBN: 978-3-540-69129-7

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