Specific Features of Descriptive Statistics with Fuzzy Random Variables

OĻegs Užga-Rebrovs, Gaļina Kuļešova

Abstract


The aim of the paper is to examine procedures of descriptive statistics in the case when the values of relevant attribute in a sample are set in the form of fuzzy categories. The paper provides alternative definitions of a fuzzy random variable, and describes corresponding procedures for calculating the analogues of location and spread parameters. The paper also presents some illustrative examples and analyses the results obtained. Based on the result analysis, practical recommendations are given on how to use procedures of fuzzy statistics.

Keywords:
Deterministic variance; fuzzy mean value; fuzzy random variable in Kwakernaak’s sense; fuzzy random variable in Puri-Ralescu’s sense; fuzzy variance

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References


L. Zadeh, “The concept of a linguistic variable and its application to approximate Reasoning”, Inform. Sci., vol. 8, no. 3, pp. 199–249, 1975. https://doi.org/10.1016/0020-0255(75)90036-5

H. Kwakernaak, “Fuzzy Random Variables–I. Definitions and Theorems”, Information Sciences, vol. 15, no. 1, pp. 1–29, 1978. https://doi.org/10.1016/0020-0255(78)90019-1

H. Kwakernaak, “Fuzzy Random Variables–II. Algorithms and Examples for the Discrete Case”, Information Sciences, vol. 17, no. 3, pp. 253–278, 1979. https://doi.org/10.1016/0020-0255(79)90020-3

R. Kruse, “On the Variance of Random Sets”, Journal of Mathematical Analysis and Applications, vol. 122, no. 2, pp. 469– 473, 1987. https://doi.org/10.1016/0022-247X(87)90277-0

R. Kruse, and K. D. Meyer, Statistics with Vague Data, D. Reidel Publishing Company, Dortrecht-Boston-Lancaster-Tokyo, 1987.

https://doi.org/10.1007/978-94-009-3943-1

M. L. Puri, and D. A. Ralescu, “Fuzzy random variables”, Journal of Mathematical Analysis and Applications, vol. 114, no. 2, pp. 409– 422, 1986. https://doi.org/10.1016/0022-247X(86)90093-4

M. A. Gil, “Fuzzy Random Variables à la Kruse & Meyer and à la Puri & Ralescu: Key Differences and Coincidences”, S. Mostaghim et. al. Eds., in Frontiers in Computational Intelligence, pp. 21–29, 2018.

C. Bertoluzza, N. Corall, and A. Salas, “On a new class of distance between fuzzy numbers”, Mathware & Soft Computing, vol. 2, pp. 71– 84, 1995.

A. Blanco-Fernández, M. R. Casals, A. Colubi, N. Coral, M. Garsía-Bárzana, M. A. Gil, G. González-Rodriguez, M. T. Lopes, M. A. Lubiano, M. Montenegro, A. B. Ramos-Guajardo, S. de la Rosa de Sáa, B. Sinova, “A distance-based statistical analysis of fuzzy number-valued data”, Int. J. Approx. Reas., vol. 55, no. 7, pp. 1487–1501, 2014. https://doi.org/10.1016/j.ijar.2013.09.020

A. Colubi, R. Coppi, P. DʹUrso, M. A. Gil, “Statistics with fuzzy random variables,” METRON- Int. Journal of Statistics, vol. 3, pp. 277–303, 2007.

I. Couso, D. Dubois, S. Montes, and L. Sánchez, “On various definitions on the variance of a fuzzy random variable”, 5th Int. Symposium on Imprecise Probability: Theories and Applications, Prague, Czech Republic, 10 p. 2007.

I. Couso, and D. Dubois, “On the variability of the concept of variance for fuzzy random variables,” IEEE Trans. Fuzzy Systems, vol. 17, no. 5, pp. 1070–1080, 2009. https://doi.org/10.1109/TFUZZ.2009.2021617

I. Couso, and D. Dubois, “Statistical reasoning with set-valued information: Ontic vs. epistemic views,” International Journal of Approximate Reasoning, vol. 55, no. 7, pp. 1502–1518, 2014. https://doi.org/10.1016/j.ijar.2013.07.002

M. A. Gil, “Statistics with fuzzy data by using random fuzzy sets”, Proceedings 58th World Statistical Congress, Dublin, 2011, pp. 1283– 1290.




DOI: 10.7250/itms-2018-0017

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