Classes of fuzzy measures and distortion

Ľubica Valášková; Peter Struk

Kybernetika (2005)

  • Volume: 41, Issue: 2, page [205]-212
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Valášková, Ľubica, and Struk, Peter. "Classes of fuzzy measures and distortion." Kybernetika 41.2 (2005): [205]-212. <http://eudml.org/doc/33749>.

@article{Valášková2005,
abstract = {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.},
author = {Valášková, Ľubica, Struk, Peter},
journal = {Kybernetika},
keywords = {fuzzy measure; distorted measure; belief measure; plausibility measure; distorted measure; fuzzy measure; belief measure; plausibility measure},
language = {eng},
number = {2},
pages = {[205]-212},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Classes of fuzzy measures and distortion},
url = {http://eudml.org/doc/33749},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Valášková, Ľubica
AU - Struk, Peter
TI - Classes of fuzzy measures and distortion
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 2
SP - [205]
EP - 212
AB - 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.
LA - eng
KW - fuzzy measure; distorted measure; belief measure; plausibility measure; distorted measure; fuzzy measure; belief measure; plausibility measure
UR - http://eudml.org/doc/33749
ER -

References

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  1. Aumann R. J., Shapley L. S., Values of Non-Atomic Games, Princeton University Press, Princeton 1974 Zbl0311.90084MR0378865
  2. Bronevich A. G., Aggregation operators of fuzzy measures, Properties of inheritance, submitted 
  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 MR1987678
  4. Denneberg D., Non-Additive Measure and Integral, Kluwer Academic Publishers, Dordrecht 1994 Zbl0968.28009MR1320048
  5. Dubois D., Prade H., Possibility Theory, Plenum Press, New York 1998 Zbl1213.68620MR1104217
  6. Dzjadyk V. K., Vvedenie v teoriju ravnomernogo približenia funkcij polinomami, Nauka, Moskva 1977 
  7. Pap E., Null-Additive Set Functions, Kluwer Academic Publishers, Dordrecht – Boston – London and Ister Science, Bratislava 1995 Zbl1003.28012MR1368630
  8. (ed.) E. Pap, Handbook on Measure Theory, Elsevier, Amsterdam 2002 
  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 Zbl1109.28303
  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 
  11. Wang Z., Klir G., Fuzzy Measure Theory, Plenum Press, New York – London 1992 Zbl0812.28010MR1212086

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