Geodesic
A nonstandard modification of Dempster combination rule
Kybernetika, Tome 38 (2002) no. 1, pp. 1-12 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

It is a well-known fact that the Dempster combination rule for combination of uncertainty degrees coming from two or more sources is legitimate only if the combined empirical data, charged with uncertainty and taken as random variables, are statistically (stochastically) independent. We shall prove, however, that for a particular but large enough class of probability measures, an analogy of Dempster combination rule, preserving its extensional character but using some nonstandard and boolean-like structures over the unit interval of real numbers, can be obtained without the assumption of statistical independence of input empirical data charged with uncertainty.
It is a well-known fact that the Dempster combination rule for combination of uncertainty degrees coming from two or more sources is legitimate only if the combined empirical data, charged with uncertainty and taken as random variables, are statistically (stochastically) independent. We shall prove, however, that for a particular but large enough class of probability measures, an analogy of Dempster combination rule, preserving its extensional character but using some nonstandard and boolean-like structures over the unit interval of real numbers, can be obtained without the assumption of statistical independence of input empirical data charged with uncertainty.
Classification : 60A05, 60E05, 68T37
Keywords: nonstandard probability; Boolean algebra 
@article{KYB_2002_38_1_a0,
     author = {Kramosil, Ivan},
     title = {A nonstandard modification of {Dempster} combination rule},
     journal = {Kybernetika},
     pages = {1--12},
     year = {2002},
     volume = {38},
     number = {1},
     mrnumber = {1899844},
     zbl = {1265.68268},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2002_38_1_a0/}
}
TY  - JOUR
AU  - Kramosil, Ivan
TI  - A nonstandard modification of Dempster combination rule
JO  - Kybernetika
PY  - 2002
SP  - 1
EP  - 12
VL  - 38
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/KYB_2002_38_1_a0/
LA  - en
ID  - KYB_2002_38_1_a0
ER  - 
%0 Journal Article
%A Kramosil, Ivan
%T A nonstandard modification of Dempster combination rule
%J Kybernetika
%D 2002
%P 1-12
%V 38
%N 1
%U http://geodesic.mathdoc.fr/item/KYB_2002_38_1_a0/
%G en
%F KYB_2002_38_1_a0
Kramosil, Ivan. A nonstandard modification of Dempster combination rule. Kybernetika, Tome 38 (2002) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/KYB_2002_38_1_a0/

[1] Dubois D., Prade H.: Théorie de Possibilités – Applications à la Représentation de Connaissances en Informatique. Mason, Paris 1985

[2] Faure R., Heurgon E.: Structures Ordonnées et Algébres de Boole. Gauthier–Villars, Paris 1971 | MR | Zbl

[3] Halmos P. R.: Measure Theory. D. van Nostrand, New York – Toronto – London 1950 | MR | Zbl

[4] Kramosil I.: Believeability and plausibility functions over infinite sets. Internat. J. Gen. Systems 23 (1994), 2, 173–198 | DOI

[5] Kramosil I.: A probabilistic analysis of Dempster combination rule. In: The Logica Yearbook 1997, Prague 1997, pp. 175–187

[6] Kramosil I.: Probabilistic Analysis of Belief Functions. Kluwer Academic / Plenum Publishers, New York – Boston – Dordrecht – London – Moscow 2001

[7] Shafer G.: A Mathematical Theory of Evidence. Princeton Univ. Press, Princeton 1976 | MR | Zbl

[8] Sikorski R.: Boolean Algebras. Springer–Verlag, Berlin – Göttingen – Heidelberg 1960 | MR | Zbl