| Title:
|
Why $\lambda $-additive (fuzzy) measures? (English) |
| Author:
|
Chiţescu, Ion |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
246-254 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper is concerned with generalized (i. e. monotone and possibly non-additive) measures. A discussion concerning the classification of these measures, according to the type and amount of non-additivity, is done. It is proved that $\lambda$-additive measures appear naturally as solutions of functional equations generated by the idea of (possible) non additivity. (English) |
| Keyword:
|
generalized measure (probability) |
| Keyword:
|
$\lambda $-additive measure |
| Keyword:
|
functional equation |
| MSC:
|
28A23 |
| MSC:
|
28E05 |
| MSC:
|
28E10 |
| MSC:
|
39B05 |
| MSC:
|
39B22 |
| MSC:
|
60A86 |
| idZBL:
|
Zbl 06487076 |
| idMR:
|
MR3350559 |
| DOI:
|
10.14736/kyb-2015-2-0246 |
| . |
| Date available:
|
2015-06-19T15:17:23Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144295 |
| . |
| Reference:
|
[1] Aczel, J.: Lectures on Functional Equations and Their Applications..Dover Publications, Inc. Mineola, New York 2006. Zbl 0139.09301 |
| Reference:
|
[2] Sugeno, M.: Theory of Fuzzy Integrals and Its Applications..Doctoral Dissertation, Tokyo Institute of Technology, 1974. |
| Reference:
|
[3] Wang, Z.: Une classe de mesures floues - les quasi-mesures..BUSEFAL 6 (1981), 28-37. |
| Reference:
|
[4] Wang, Z., Klir, G.: Generalized Measure Theory..Springer (IFSR Internat. Ser. Systems Sci. Engrg. 25) (2009). Zbl 1184.28002, MR 2453907, 10.1007/978-0-387-76852-6 |
| . |
