WMethod {FuzzyResampling}

w method for resampling triangular and trapezoidal fuzzy numbers

Description

WMethod returns the secondary (bootstrapped) sample and uses the resampling scheme based on the special w density which is related to the left ends of the cores and increments (i.e. length of the core, left and right increment of the support) of the fuzzy variables from the initial sample (the d method, see (Romaniuk and Hryniewicz, 2019)).

Usage

WMethod(initialSample, b = n, increases = FALSE)

Arguments

initialSample

Initial sample of triangular or trapezoidal fuzzy numbers.

b

The number of fuzzy values in the resampled (secondary) sample. If this parameter is not specified, the number of values in the initial sample is used. The parameter should be integer value more than 0.

increases

If TRUE is used, then the initial sample should consist of the fuzzy numbers in the form: left increment of the support, left end of the core, right end of the core, right increment of the support. Otherwise, the default value FALSE is used and the fuzzy numbers should be given in the form: left end of the support, left end of the core, right end of the core, right end of the support.

Details

The initial sample should consist of triangular or trapezoidal fuzzy numbers, given as a single vector or a whole matrix. In each row, there should be a single fuzzy number in one of the forms:

1. left end of the support, left end of the core, right end of the core, right end of the support, or

2. left increment of the support, left end of the core, right end of the core, right increment of the support.

In this second case, the parameter increases=TRUE has to be used.

The resampling procedure produces b fuzzy values. During the first step, the four values are randomly generated using the special w density: left end of the core, length of the core, left and right increment of the support. This w density is calculated based on the whole fuzzy sample. Then the new fuzzy variable, which preserves the above-mentioned characteristics, is created. If the parameter b is not specified, it is equal to the length of the initial sample. The output is given in the same form as the initial sample.

Value

This function returns matrix with b rows of double values. In each row, there is a single resampled fuzzy number. These fuzzy numbers have the same form as the values from the initial sample depending on the provided parameter increases.

References

Romaniuk, M., Hryniewicz, O. (2019) Interval-based, nonparametric approach for resampling of fuzzy numbers Soft Computing, 23 (14), pp. 5883-5903

See Also

ClassicalBootstrap, EWMethod for the EW method, VAFMethod for the VAF method, VAAMethod for the VAA method

Other resampling functions: ClassicalBootstrap(), DMethod(), EWMethod(), VAAMethod(), VAFMethod(), VAMethod()

Examples

# prepare some fuzzy numbers (first type of the initial sample)

fuzzyValues <- matrix(c(0.25,0.5,1,1.25,0.75,1,1.5,2.2,-1,0,0,2),
ncol = 4,byrow = TRUE)

# generate the secondary sample using the w method

set.seed(12345)

WMethod(fuzzyValues)

WMethod(fuzzyValues,b=4)

# prepare some fuzzy numbers (second type of the initial sample)

fuzzyValuesInc <- matrix(c(0.25,0.5,1,0.25,0.25,1,1.5,0.7,1,0,0,2),
ncol = 4,byrow = TRUE)

# generate the secondary sample using the w method

WMethod(fuzzyValuesInc,increases = TRUE)

WMethod(fuzzyValuesInc,b=4,increases = TRUE)