Geodesic
Admissible and Bayes decisions with fuzzy-valued losses
Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 166-174

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: fuzzy sets, admissible decisions, Bayes decisions. 
@article{DM_2021_33_2_a11,
     author = {A. S. Shvedov},
     title = {Admissible and {Bayes} decisions with fuzzy-valued losses},
     journal = {Diskretnaya Matematika},
     pages = {166--174},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_2_a11/}
}
TY  - JOUR
AU  - A. S. Shvedov
TI  - Admissible and Bayes decisions with fuzzy-valued losses
JO  - Diskretnaya Matematika
PY  - 2021
SP  - 166
EP  - 174
VL  - 33
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2021_33_2_a11/
LA  - ru
ID  - DM_2021_33_2_a11
ER  - 
%0 Journal Article
%A A. S. Shvedov
%T Admissible and Bayes decisions with fuzzy-valued losses
%J Diskretnaya Matematika
%D 2021
%P 166-174
%V 33
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2021_33_2_a11/
%G ru
%F DM_2021_33_2_a11
A. S. Shvedov. Admissible and Bayes decisions with fuzzy-valued losses. Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 166-174. http://geodesic.mathdoc.fr/item/DM_2021_33_2_a11/