Abstract
In a previous paper the fuzzy characterizing function of a random fuzzy number was introduced as an extension of the moment generating function of a real-valued random variable. Properties of the fuzzy characterizing function have been examined, among them, the crucial one proving that it unequivocally determines the distribution of a random fuzzy number in a neighborhood of 0. This property suggests to consider the empirical fuzzy characterizing function as a tool to measure the dissimilarity between the distributions of two random fuzzy numbers, and its expected descriptive potentiality is illustrated by means of a real-life example.
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Acknowledgments
Authors are grateful to Colegio San Ignacio in Oviedo-Asturias (Spain) for allowing us to collect the data in the real-life example. The research in this paper has been partially supported by/benefited from Principality of Asturias Grant GRUPIN14-101, and the Spanish Ministry of Economy and Competitiveness Grants MTM2015-63971-P and MTM2013-44212-P. Their financial support is gratefully acknowledged.
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Lubiano, M.A., Gil, M.Á., Sinova, B., Casals, M.R., López, M.T. (2017). Measuring the Dissimilarity Between the Distributions of Two Random Fuzzy Numbers. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_40
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DOI: https://doi.org/10.1007/978-3-319-42972-4_40
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