| Title:
|
Non additive ordinal relations representable by lower or upper probabilities (English) |
| Author:
|
Capotorti, Andrea |
| Author:
|
Coletti, Giulianella |
| Author:
|
Vantaggi, Barbara |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
[79]-90 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize (in terms of necessary and sufficient conditions) binary relations representable by a lower probability. Such relations can be non- additive (as the relations representable by a probability) and also not “partially monotone” (as the relations representable by a belief function). Moreover we characterize relations representable by upper probabilities and those representable by plausibility. In fact the conditions characterizing these relations are not immediately deducible by means of “dual” conditions given on the contrary events, like in the numerical case. (English) |
| Keyword:
|
coherent lower probability |
| MSC:
|
03B48 |
| MSC:
|
68T30 |
| MSC:
|
68T37 |
| idZBL:
|
Zbl 1274.68518 |
| idMR:
|
MR1619057 |
| . |
| Date available:
|
2009-09-24T19:13:54Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135187 |
| . |
| Reference:
|
[1] Coletti G.: Coherent qualitative probability.J. Math. Psych. 34 (1990), 297–310 Zbl 0713.60003, MR 1068441, 10.1016/0022-2496(90)90034-7 |
| Reference:
|
[2] Coletti G.: Non additive ordinal relations representable by conditional probabilities and their use in expert systems.In: Proceedings 6th International Conference IPMU’96, 1 (1996), pp. 43–48 |
| Reference:
|
[3] Dubois D.: Belief structure, possibility theory and decomposable confidence measures on finite sets.Comput. Artificial Intelligence 5 (1986), 5, 403–416 |
| Reference:
|
[4] Finetti B. de: Sul Significato Soggettivo della Probabilità.Fundamenta Matematicae 17 (1931), 293–329 Zbl 0003.16303 |
| Reference:
|
[5] Koopman B. O.: The axioms and algebra of intuitive probability.Ann. Math. 41 (1940), 269–292 Zbl 0024.05001, MR 0001474, 10.2307/1969003 |
| Reference:
|
[6] Kraft C. H., Pratt J. W., Seidenberg A.: Intuitive probabilities on finite sets.Ann. Math. Statist. 30 (1959), 408–419 MR 0102850, 10.1214/aoms/1177706260 |
| Reference:
|
[7] Regoli G.: Rational Comparison and Numerical Representation.Decision Theory and Decision Analysis: Trends and challenges. Academic Publishers, Dordrecht 1994 |
| Reference:
|
[8] Scott D.: Measurement structures and linear inequalities.J. Math. Psych. 1 (1964), 233–247 Zbl 0129.12102, 10.1016/0022-2496(64)90002-1 |
| Reference:
|
[9] Walley P.: Statistical Reasoning with Imprecise Probabilities.Chapman & Hall, London 1990 Zbl 0732.62004, MR 1145491 |
| Reference:
|
[10] Wong S. K. M., Yao Y. Y., Bollmann P., Bürger H. C.: Axiomatization of qualitative belief structure.IEEE Trans. Systems Man Cybernet. 21 (1991), 726–734 Zbl 0737.60006, MR 1143669, 10.1109/21.108290 |
| . |
