Abstract
The R package SAFD (Statistical Analysis of Fuzzy Data) provides basic tools for elementary statistics with one dimensional Fuzzy Data in the form of polygonal fuzzy numbers. In particular, the package contains functions for the standard operations on the class of fuzzy numbers (sum, scalar product, mean, Hukuhara difference, quantiles) as well as for calculating (Bertoluzza) distance, sample variance, sample covariance, sample correlation, and the Dempster-Shafer (levelwise) histogram. Moreover SAFD facilitates functions for the simulation of fuzzy random variables, for bootstrap tests for the equality of means as well as a function for linear regression given trapezoidal fuzzy data. The aim of this paper is to explain the functionality of the package and to illustrate its usage by various examples.
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References
Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers. Mathware & Soft Comput. 2, 71–84 (1995)
Colubi, A.: Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy- and real-valued data. Fuzzy Sets and Systems 160(3), 344–356 (2009)
González-Rodríguez, G., Blanco, A., Colubi, A., Lubiano, M.A.: Estimation of a simple linear regression model for fuzzy random variables. Fuzzy Sets and Systems 160(3), 357–370 (2009)
González-Rodríguez, G., Colubi, A., Trutschnig, W.: Simulation of fuzzy random variables. Information Sciences 179(5), 642–653 (2009)
Hesketh, B., Hesketh, T., Hansen, J.-I., Goranson, D.: Use of fuzzy variables in developing new scales from the strong interest inventory. J. Counseling Psychology 42, 85–99 (1995)
Lubiano, M.A., Trutschnig, W.: ANOVA for Fuzzy Random Variables Using the R-package SAFD. In: Borgelt, C., et al. (eds.) Combining Soft Computing and Statistical Methods in Data Analysis, pp. 449–456. Springer, Heidelberg (2010)
Möller, B., Beer, M.: Fuzzy Randomness — Uncertainty in Civil Engineering and Computational Mechanics. Springer, Berlin (2004)
Puri, M.L., Ralescu, D.A.: Fuzzy random variables. J. Math. Anal. Appl. 114, 409–422 (1986)
Sinova, B., Gil, M.A., Colubi, A., Van Aelst, S.: The median of a random fuzzy number. The 1-norm distance approach. Fuzzy Sets and Systems (to appear, 2012)
Trutschnig, W.: A strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy-valued probability. Fuzzy Sets and Systems 159(3), 259–269 (2008)
Trutschnig, W., González-Rodríguez, G., Colubi, A., Gil, M.A.: A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread. Information Sciences 179(23), 3964–3972 (2009)
Viertl, R., Hareter, D.: Beschreibung und Analyse unscharfer Information: Statistische Methoden für unscharfe Daten. Springer, Wien New York (2006)
Zadeh, L.A.: 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. 9, 43–80 (1975)
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Trutschnig, W., Lubiano, M.A., Lastra, J. (2013). SAFD — An R Package for Statistical Analysis of Fuzzy Data. In: Borgelt, C., Gil, M., Sousa, J., Verleysen, M. (eds) Towards Advanced Data Analysis by Combining Soft Computing and Statistics. Studies in Fuzziness and Soft Computing, vol 285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30278-7_10
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DOI: https://doi.org/10.1007/978-3-642-30278-7_10
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