Abstract
In this paper we investigate different mappings of fuzzy measures in the framework of probabilistic approach. Usually these mappings in the decision-making theory are called convolution (aggregation) operators [1,2]. We study what kind of restrictions is required to the convolution operator that one family of fuzzy measures (for example belief measures) is mapped to the same family.
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References
Dubois D. and Prade, H. (1988) Possibility Theory. Plenum Press, New York.
Grabisch, M., Nguyen, H.T., and Walker, E.A. (1995). Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference. Kluwer Academic Publishers, New York.
Bronevich, A.G. and Karkishchenko, A.N. (2002) The structure of fuzzy measure families induced by upper and lower probabilities. Statistical modeling, analysis and management of fuzzy data. Heidelberg; New York: Physica-verl., 160–172.
Dempster, A.P. (1967) Upper and lower probabilities induced by multivalued mapping. Ann. Math. Statist., 38, 325–339
Walley, P. (1991) Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, London.
Sugeno, M. (1972) Fuzzy measure and fuzzy integral. Trans. SICE, 8, 95–102
Shafer, G. (1976) A mathematical theory of evidence. Princeton University Press, Princeton, N.J.
Chateauneuf, A. and Jaffray, J.Y. (1989) Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion, Mathematical Social Sciences, 17, 263–283.
Gelfond, A.O. (1967) Calculi of finite differences. “Nauka” Press, Moscow. (In Russian)
Fihtengoltz, G. (1969) Course of the differential and integral calculi, V.1, “Nauka” Press, Moscow. (In Russian)
Murofushi, T., Sugeno, M. (1989) An interpretation of fuzzy measure and Choquet integral as an integral with respect to fuzzy measure. Fuzzy sets and Systems, 29, 229–235.
Mesiar R. (1995) Choquet-like integrals, J. Math. Anal. Appl., 194, 477–488.
Dubois, D., Farinas del Cerro, Herzig, A., Prade, H. (1994) An original view of independence with application to plausible reasoning. Proceedings of 10-th conference “Uncertainty in Artificial reasoning”, 195–203.
De Cooman, G. Possibility Theory I-III.International journal of General systems, 25, 291–371.
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Bronevich, A.G., Lepskiy, A.E. (2002). Operators for Convolution of Fuzzy Measures. In: Grzegorzewski, P., Hryniewicz, O., Gil, M.Á. (eds) Soft Methods in Probability, Statistics and Data Analysis. Advances in Intelligent and Soft Computing, vol 16. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1773-7_5
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DOI: https://doi.org/10.1007/978-3-7908-1773-7_5
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1526-9
Online ISBN: 978-3-7908-1773-7
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