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Article

Keywords:
fuzzy measure; distorted measure; belief measure; plausibility measure
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.
References:
[1] Aumann R. J., Shapley L. S.: Values of Non-Atomic Games. Princeton University Press, Princeton 1974 MR 0378865 | Zbl 0311.90084
[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 1987678
[4] Denneberg D.: Non-Additive Measure and Integral. Kluwer Academic Publishers, Dordrecht 1994 MR 1320048 | Zbl 0968.28009
[5] Dubois D., Prade H.: Possibility Theory. Plenum Press, New York 1998 MR 1104217 | Zbl 1213.68620
[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 1368630 | Zbl 1003.28012
[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 1109.28303
[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 MR 1212086 | Zbl 0812.28010
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