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Admissible and Bayes decisions with fuzzy-valued losses

  • Alexey S. Shvedov EMAIL logo
Published/Copyright: April 13, 2022

Abstract

Some results of classical statistical decision theory are generalized by means of the theory of fuzzy sets. The concepts of an admissible decision in the restricted sense, an admissible decision in the broad sense, a Bayes decision in the restricted sense, and a Bayes decision in the broad sense are introduced. It is proved that any Bayes decision in the broad sense with positive prior discrete density is admissible in the restricted sense. The class of Bayes decisions is shown to be complete under certain conditions on the loss function. Problems with a finite set of possible states are considered.


Originally published in Diskretnaya Matematika (2021) 33, №2, 166–174 (in Russian).


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Received: 2018-06-30
Revised: 2021-04-10
Published Online: 2022-04-13
Published in Print: 2022-04-26

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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