Classes of fuzzy measures and distortion
Kybernetika, Tome 41 (2005) no. 2, pp. 205-212 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 03E72, 28E10
Keywords: fuzzy measure; distorted measure; belief measure; plausibility measure
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Valášková, Ľubica; Struk, Peter. Classes of fuzzy measures and distortion. Kybernetika, Tome 41 (2005) no. 2, pp. 205-212. http://geodesic.mathdoc.fr/item/KYB_2005_41_2_a6/

[1] Aumann R. J., Shapley L. S.: Values of Non-Atomic Games. Princeton University Press, Princeton 1974 | MR | Zbl

[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 | MR

[4] Denneberg D.: Non-Additive Measure and Integral. Kluwer Academic Publishers, Dordrecht 1994 | MR | Zbl

[5] Dubois D., Prade H.: Possibility Theory. Plenum Press, New York 1998 | MR | Zbl

[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 | MR | Zbl

[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 | Zbl

[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 | MR | Zbl