| Title:
|
A nonstandard modification of Dempster combination rule (English) |
| Author:
|
Kramosil, Ivan |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
[1]-12 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
nonstandard probability |
| Keyword:
|
Boolean algebra |
| MSC:
|
60A05 |
| MSC:
|
60E05 |
| MSC:
|
68T37 |
| idZBL:
|
Zbl 1265.68268 |
| idMR:
|
MR1899844 |
| . |
| Date available:
|
2009-09-24T19:43:30Z |
| Last updated:
|
2015-03-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135443 |
| . |
| Reference:
|
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| Reference:
|
[2] Faure R., Heurgon E.: Structures Ordonnées et Algébres de Boole.Gauthier–Villars, Paris 1971 Zbl 0219.06001, MR 0277440 |
| Reference:
|
[3] Halmos P. R.: Measure Theory.D. van Nostrand, New York – Toronto – London 1950 Zbl 0283.28001, MR 0033869 |
| Reference:
|
[4] Kramosil I.: Believeability and plausibility functions over infinite sets.Internat. J. Gen. Systems 23 (1994), 2, 173–198 10.1080/03081079508908038 |
| Reference:
|
[5] Kramosil I.: A probabilistic analysis of Dempster combination rule.In: The Logica Yearbook 1997, Prague 1997, pp. 175–187 |
| Reference:
|
[6] Kramosil I.: Probabilistic Analysis of Belief Functions.Kluwer Academic / Plenum Publishers, New York – Boston – Dordrecht – London – Moscow 2001 |
| Reference:
|
[7] Shafer G.: A Mathematical Theory of Evidence.Princeton Univ. Press, Princeton 1976 Zbl 0359.62002, MR 0464340 |
| Reference:
|
[8] Sikorski R.: Boolean Algebras.Springer–Verlag, Berlin – Göttingen – Heidelberg 1960 Zbl 0191.31505, MR 0126393 |
| . |
