SAFD-package: Statistical Analysis of Fuzzy Data
Description
The aim of the package is to provide some basic functions for doing statistics with
one-dimensional Fuzzy Data (in the form of polygonal fuzzy numbers).Details
ll{
Package: SAFD
Type: Package
Version: 0.02
Date: 2009-10-15
License: GPL (>=2)
LazyLoad: yes
}
The package allows to work with polygonal fuzzy numbers, being represented as data frames with columns x and alpha (equidistant alpha levels in [0,1]). SAFD contains functions for the basic operations on the class of fuzzy numbers (sum, scalar product, mean, Hukuhara difference) as well as for calculating (Bertoluzza-) distance, sample variance, sample covariance, sample correlation, and the Dempster-Shafer (levelwise) histogram. Moreover a function to simulate fuzzy random variables, bootstrap tests for the equality of means, and a function to do linear regression given trapezoidal fuzzy data is included.References
[1] Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers, Mathware Soft Comput., 2, pp:71-84 (1995)
[2] 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), pp. 344-356 (2009)
[3] Gil, M.A., Lopez, M.T., Lubiano, M.A., Montenegro, M.: Regression and correlation analyses of a linear relation between random intervals, Test, 10(1), pp. 183-201 (2001)
[4] Gil, M.A.; Montenegro, M.; Gonzalez-Rodriguez, G.; Colubi, A.; Casals, R.: Bootstrap approach to the multi-sample test of means with imprecise data, Computational Statistics and Data Analysis, 51(1), pp. 148-162 (2006)
[5] Gonzalez-Rodriguez, 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), pp. 357-370 (2009)
[6] Gonzalez-Rodriguez, G., Colubi, A., Trutschnig, W.: Simulation of fuzzy random variables, Information Sciences, 179(5), pp. 642-653 (2009)
[7] Montenegro, M., Colubi, A., Casals, M.R., Gil, M.A.: Asymptotic and bootstrap techniques for testing the expected value of a fuzzy random variable, Metrika, 59, pp. 31-49 (2004)
[8] Montenegro, M., Casals, M.R., Lubiano, M.A., Gil, M.A.: Two-sample hypothesis tests of means of a fuzzy random variable, Information Sciences, Vol. 133(1-2), pp. 89-100 (2001)
[9] Trutschnig, W., A strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy-valued probability, Fuzzy Sets and Systems, Vol. 159, nr 3, pp. 259-269 (2008)
[10] Trutschnig, W., Gonzalez-Rodriguez, 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), pp. 3964-3972 (2009)
[11] Viertl, R., Hareter, D.: Beschreibung und Analyse unscharfer Information: Statistische Methoden fuer unscharfe Daten, Springer Wien New York, 2006See Also
http://bellman.ciencias.uniovi.es/SMIRE/