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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References
Couso I, Dubois D (2014) Statistical reasoning with set-valued information: Ontic vs. epistemic views. Int J Appr Reas 55(7):1502–1518
Diamond P, Kloeden P (1999) Metric spaces of fuzzy sets. Fuzzy Sets Syst 100:63–71
Lubiano MA, De la Rosa de Sáa S, Montenegro M, Sinova B, Gil, MA (2016) Descriptive analysis of responses to items in questionnaires. Why not using a fuzzy rating scale? Inform Sci 360:131–148
Lubiano MA, Montenegro M, Sinova B, De la Rosa de Sáa S, Gil MA (2016) Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications. Eur J Oper Res 251:918–929
Meintanis SG (2007) A KolmogorovSmirnov type test for skew normal distributions based on the empirical moment generating function. J Stat Plan Infer 137:2681–2688
Mora J, Mora-López L (2010) Comparing distributions with bootstrap techniques: an application to global solar radiation. Math Comp Simul 81:811–819
Nguyen HT (1978) A note on the extension principle for fuzzy sets. J Math Anal Appl 64:369–380
Puri ML, Ralescu DA (1986) Fuzzy random variables. J Math Anal Appl 114:409–422
Sinova B, Casals MR, Gil MA, Lubiano MA (2015) The fuzzy characterizing function of the distribution of a random fuzzy number. Appl Math Model 39(14):4044–4056
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning, Part 1. Inform Sci 8:199–249; Part 2. Inform Sci 8:301–353; Part 3. Inform Sci 8:43–80
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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