| Title:
|
Many-dimensional observables on Łukasiewicz tribe: constructions, conditioning and conditional independence (English) |
| Author:
|
Kroupa, Tomáš |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
[451]-468 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Probability on collections of fuzzy sets can be developed as a generalization of the classical probability on $\sigma $-algebras of sets. A Łukasiewicz tribe is a collection of fuzzy sets which is closed under the standard fuzzy complementation and under the pointwise application of the Łukasiewicz t-norm to countably many fuzzy sets. An observable is a fuzzy set-valued mapping defined on a $\sigma $-algebra of sets and satisfying some additional properties; formally, the role of an observable is in a sense analogous to that of a random variable in classical probability theory. This article aims at studying and surveying some properties of observables on a Łukasiewicz tribe of fuzzy sets with a special focus on many-dimensional observables. Namely, the definition and basic construction techniques of observables are discussed. A method for a reasonable construction and interpretation of a joint observable is proposed. Further, the contribution contains results concerning conditioning of observables. We continue in our study [kroupaSC] of conditional independence in this framework and conclude that semi-graphoid properties are preserved. (English) |
| Keyword:
|
state |
| Keyword:
|
observable |
| Keyword:
|
tribe of fuzzy sets |
| Keyword:
|
conditional independence |
| MSC:
|
03E72 |
| MSC:
|
06D35 |
| MSC:
|
06D39 |
| MSC:
|
60A86 |
| MSC:
|
60B99 |
| idZBL:
|
Zbl 1249.60004 |
| idMR:
|
MR2180357 |
| . |
| Date available:
|
2009-09-24T20:10:25Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135669 |
| . |
| Reference:
|
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