Statistical Papers

, Volume 32, Issue 1, pp 115–122 | Cite as

On Bayes' theorem for fuzzy data

  • R. Viertl
  • H. Hule


There are some ideas concerning a generalization of Bayes' theorem to the situation of fuzzy data. Some of them are given in the references [1], [5], and [7]. But the proposed methods are not generalizations in the sense of the probability content of Bayes' theorem for precise data. In the present paper a generalization of Bayes' theorem to the case of fuzzy data is described which contains Bayes' theorem for precise data as a special case and allows to use the information in fuzzy data in a coherent way. Moreover a generalization of the concept of HPD-regions is explained which makes it possible to model and analyze the situation of fuzzy data. Also a generalization of the concept of predictive distributions is given in order to calculate predictive densities based on fuzzy sample information.


Fuzzy Number Precise Data Predictive Distribution Fuzzy Data Predictive Density 
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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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • R. Viertl
    • 1
  • H. Hule
    • 1
  1. 1.Institut für Statistik und WahrscheinlichkeitstheorieTechnische Universität WienWienAustria

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