FuzzyResampling-package: FuzzyResampling: Resampling Methods for Triangular and...

In FuzzyResampling: Resampling Methods for Triangular and Trapezoidal Fuzzy Numbers

FuzzyResampling: Resampling Methods for Triangular and Trapezoidal Fuzzy Numbers

Description

The classical (i.e. Efron's, see Efron and Tibshirani (1994, ISBN:978-0412042317) "An Introduction to the Bootstrap") bootstrap is widely used for both the real (i.e. "crisp") and fuzzy data. The main aim of the algorithms implemented in this package is to overcome a problem with repetition of a few distinct values and to create fuzzy numbers, which are "similar" (but not the same) to values from the initial sample. To do this, different characteristics of triangular/trapezoidal numbers are kept (like the value, the ambiguity, etc., see Grzegorzewski et al. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2991/eusflat-19.2019.68")}, Grzegorzewski et al. (2020) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2991/ijcis.d.201012.003")}, Grzegorzewski et al. (2020) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.34768/amcs-2020-0022")}, Grzegorzewski and Romaniuk (2022) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-3-030-95929-6_3")}, Romaniuk and Hryniewicz (2019) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s00500-018-3251-5")}). Some additional procedures related to these resampling methods are also provided, like calculation of the Bertoluzza et al.'s distance (aka the mid/spread distance, see Bertoluzza et al. (1995) "On a new class of distances between fuzzy numbers") and estimation of the p-value of the one- and two- sample bootstrapped test for the mean (see Lubiano et al. (2016, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ejor.2015.11.016")})). Additionally, there are procedures which randomly generate trapezoidal fuzzy numbers using some well-known statistical distributions.

The following procedures are available in the library

• ClassicalBootstrap - classical approach based on Efron's method,

• VAMethod - resampling method which preserves the value and ambiguity,

• EWMethod - resampling method which preserves the expected value and width,

• VAAMethod - resampling method which preserves the value, left-hand and right-hand ambiguities,

• VAFMethod - resampling method which preserves the value, ambiguity and fuzziness,

• DMethod - resampling method which preserves the left end of the cores and increments,

• WMethod - resampling method which uses the special w density to "smooth" the output fuzzy value,

• GeneratorNU - generation of the initial sample using the normal and uniform distributions,

• GeneratorNExpUU - generation of the initial sample using the normal, exponential and uniform distributions,

• GeneratorFuzzyNumbers - generation of the initial sample using various random distributions,

• OneSampleCTest - estimation of the p-value of the one-sample test for the mean,

• TwoSampleCTest - estimation of the p-value of the two-sample test for the mean,

• SEResamplingMean - estimation of the standard error or the mean-squared error for the mean,

• BertoluzzaDistance - calculation of the Bertoluzza et al.'s distance (aka the mid/spread distance),

• ComparisonOneSampleCTest - comparison of resampling methods based on percentage of rejections for the one-sample C-test,

• ComparisonSEMean - comparison of resampling methods based on the SE/MSE for the mean,

• ComparePowerOneSampleCTest - comparison of resampling methods based on percentage of rejections for the one-sample C-test,

Author(s)

Maintainer: Maciej Romaniuk [e-mail]

Authors:

• Przemyslaw Grzegorzewski [e-mail]

• Olgierd Hryniewicz [e-mail]

See Also

Useful links:

• https://github.com/mroman-ibs/FuzzyResampling

• Report bugs at https://github.com/mroman-ibs/FuzzyResampling/issues

FuzzyResampling documentation built on Oct. 4, 2024, 5:11 p.m.