| Title:
|
Classes of fuzzy measures and distortion (English) |
| Author:
|
Valášková, Ľubica |
| Author:
|
Struk, Peter |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
[205]-212 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Distortion of fuzzy measures is discussed. A special attention is paid to the preservation of submodularity and supermodularity, belief and plausibility. Full characterization of distortion functions preserving the mentioned properties of fuzzy measures is given. (English) |
| Keyword:
|
fuzzy measure |
| Keyword:
|
distorted measure |
| Keyword:
|
belief measure |
| Keyword:
|
plausibility measure |
| MSC:
|
03E72 |
| MSC:
|
28E10 |
| idZBL:
|
Zbl 1249.28032 |
| idMR:
|
MR2138768 |
| . |
| Date available:
|
2009-09-24T20:08:12Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135650 |
| . |
| Reference:
|
[1] Aumann R. J., Shapley L. S.: Values of Non-Atomic Games.Princeton University Press, Princeton 1974 Zbl 0311.90084, MR 0378865 |
| Reference:
|
[2] Bronevich A. G.: Aggregation operators of fuzzy measures.Properties of inheritance, submitted |
| Reference:
|
[3] Bronevich A. G., Lepskiy A. E.: Operators for Convolution of Fuzzy Measures.In: Soft Methods in Probability, Statistics and Data Analysis, Advances in Soft Computing, Physica–Verlag, Heidelberg 2002, pp. 84–91 MR 1987678 |
| Reference:
|
[4] Denneberg D.: Non-Additive Measure and Integral.Kluwer Academic Publishers, Dordrecht 1994 Zbl 0968.28009, MR 1320048 |
| Reference:
|
[5] Dubois D., Prade H.: Possibility Theory.Plenum Press, New York 1998 Zbl 1213.68620, MR 1104217 |
| Reference:
|
[6] Dzjadyk V. K.: Vvedenie v teoriju ravnomernogo približenia funkcij polinomami.Nauka, Moskva 1977 |
| Reference:
|
[7] Pap E.: Null-Additive Set Functions.Kluwer Academic Publishers, Dordrecht – Boston – London and Ister Science, Bratislava 1995 Zbl 1003.28012, MR 1368630 |
| Reference:
|
[8] (ed.) E. Pap: Handbook on Measure Theory.Elsevier, Amsterdam 2002 |
| Reference:
|
[9] Struk P., Valášková Ĺ.: Preservation of distinguished fuzzy measure classes by distortion.In: Uncertainty Modelling 2003, Publishing House of STU, Bratislava 2003, pp. 48–51 Zbl 1109.28303 |
| Reference:
|
[10] Stupňanová A., Struk P.: Pessimistic and optimistic fuzzy measures on finite sets.In: MaGiA 2003, Publishing House of STU, Bratislava 2003, pp. 94–100 |
| Reference:
|
[11] Wang Z., Klir G.: Fuzzy Measure Theory.Plenum Press, New York – London 1992 Zbl 0812.28010, MR 1212086 |
| . |
