| Title:
|
On decision-making in possibility theory (English) |
| Author:
|
Vejnarová, Jiřina |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
457-468 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present an alternative approach to decision-making in the framework of possibility theory, based on the idea of decision-making under uncertainty. We utilize the fact, that any possibility distribution can be viewed as an upper envelope of a set of probability distributions to which well-known minimax principle is applicable. Finally, we recall also an alternative to the minimax rule, so-called local minimax principle. Local minimax principle not only allows sequential construction of decision function, but also appears to play an important role exactly in the framework of possibility theory due to its sensitivity. Furthermore, the optimality of a decision function is easily verifiable. (English) |
| Keyword:
|
possibility measures and distributions |
| Keyword:
|
upper envelopes of probability distributions |
| Keyword:
|
decision functions |
| Keyword:
|
minimax principle |
| MSC:
|
62C20 |
| MSC:
|
91B06 |
| idZBL:
|
Zbl 06487090 |
| idMR:
|
MR3391679 |
| DOI:
|
10.14736/kyb-2015-3-0457 |
| . |
| Date available:
|
2015-09-01T09:13:38Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144380 |
| . |
| Reference:
|
[1] Cozman, F. G.: Sets of probability distributions, independence, and convexity..Synthese 186 (2012), 577-600. Zbl 1275.60007, MR 2935351, 10.1007/s11229-011-9999-0 |
| Reference:
|
[2] Cooman, G. de: Possibility theory I - III..Int. J. General Systems 25 (1997), 291-371. 10.1080/03081079708945160 |
| Reference:
|
[3] Cooman, G. de, Aeyels, D.: Supremum preserving upper probabilities..Inform. Sci. 118 (1999), 173-212. Zbl 0952.60009, MR 1723220, 10.1016/s0020-0255(99)00007-9 |
| Reference:
|
[4] Engemann, K. J., Yager, R. R.: A general approach to decision making with interval probabilities..Int. J. General Systems 30 (2001), 623-647. Zbl 1018.90020, MR 1878601, 10.1080/03081070108960738 |
| Reference:
|
[5] Kramosil, I.: Decision-making under uncertainty processed by lattice/valued possibilistic measures..Kybernetika 42 (2006), 629-646. Zbl 1249.28024, MR 2296505 |
| Reference:
|
[6] Vejnarová, J.: On various criteria of optimality in probabilistic decision-making..Kybernetika 28 (1992), 5, 392-401. Zbl 0776.90006, MR 1197722 |
| . |
