Package 'FuzzyStatTraEOO'

Description

'FuzzyStatTraEOO' is an open source package for R. The aim of the package is to contain the package 'FuzzyStatTra' in Encapsulated Object Oriented Programming using R6. 'FuzzyStatTra' contains Statistical Methods for Trapezoidal Fuzzy Numbers, whose aim is to provide some basic functions for doing statistical analysis with trapezoidal fuzzy numbers. For more details, you can visit the website of the SMIRE+CoDiRE (Statistical Methods with Imprecise Random Elements and Comparison of Distributions of Random Elements) Research Group (<https://bellman.ciencias.uniovi.es/smire+codire/>). The most related paper can be found in References. Now, those functions are organized in specific classes and methods. This object-based approach is an important step in making statistical computing more accessible to users.

Details

Package: FuzzyStatTraEOO
Type: Package
Version: 1.0
Date: 2022-12-12
License: LGPL (>= 3)

For a complete list of classes and their methods call help(package="FuzzyStatTraEOO"), call ??FuzzyStatTraEOO or use the Index link below, at the end of this help window.

Author(s)

Andrea Garcia Cernuda [email protected],
Asun Lubiano [email protected] and Sara de la Rosa de Saa.

Maintainer: Andrea Garcia Cernuda [email protected]

References

• Blanco-Fernandez, A.; Casals, R.M.; Colubi, A.; Corral, N.; Garcia-Barzana, M.; Gil, M.A.; Gonzalez-Rodriguez, G.; Lopez, M.T.; Lubiano, M.A.; Montenegro, M.; Ramos-Guajardo, A.B.; de la Rosa de Saa, S.; Sinova, B.: Random fuzzy sets: A mathematical tool to develop statistical fuzzy data analysis, Iranian Journal on Fuzzy Systems 10(2), 1-28 (2013)

• De la Rosa de Saa, S.; Gil, M.A.; Gonzalez-Rodriguez, G.; Lopez, M.T.; Lubiano M.A.: Fuzzy rating scale-based questionnaires and their statistical analysis, IEEE Transactions on Fuzzy Systems 23(1), 111-126 (2015)

• De la Rosa de Sáa, S.; Lubiano, M.A.; Sinova, B.; Filzmoser, P.; Gil, M.Á.: Location-free robust scale estimates for fuzzy data, IEEE Transactions on Fuzzy Systems 29(6), 1682-1694 (2021)

• De la Rosa de Saa, S.; Lubiano M.A.; Sinova, B.; Filzmoser, P.: Robust scale estimators for fuzzy data, Advances in Data Analysis and Classification 11(4), 731-758 (2017)

• Diamond, P.; Kloeden, P.: Metric spaces of fuzzy sets, Fuzzy Sets and Systems 35, 241-249 (1990)

• Gil, M.A.; Lubiano, M.A.; De la Rosa de Saa, S.; Sinova, B.: Analyzing data from a fuzzy rating scale-based questionnaire. A case study, Psicothema 27(2), 182-191 (2015)

• Lubiano, M.A.; De la Rosa de Saa, S.; Montenegro, M.; Sinova, B.; Gil, M.A.: Descriptive analysis of responses to items in questionnaires. Why not a fuzzy rating scale?, Information Sciences 360, 131-148 (2016)

• Lubiano, M.A.; Gil, M.A.: f-Inequality indices for fuzzy random variables, in Statistical Modeling, Analysis and Management of Fuzzy Data (Bertoluzza, C., Gil, M.A., Ralescu, D.A., Eds.), Physica-Verlag, 43-63 (2002)

• Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications, European Journal of Operational Research 251, 918-929 (2016)

• Lubiano, M.A.; Salas, A.; Carleos, C.; De la Rosa de Sáa, S.; Gil, M.Á.: Hypothesis testing-based comparative analysis between rating scales for intrinsically imprecise data, International Journal of Approximate Reasoning 88, 128-147 (2017)

• Lubiano, M.A.; Salas, A.; Gil, M.Á.: A hypothesis testing-based discussion on the sensitivity of means of Fuzzy data with respect to data shape, Fuzzy Sets and Systems 328(1), 54-69 (2017)

• Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: A generalized L1-type metric between fuzzy numbers for an approach to central tendency of fuzzy data, Information Sciences 242, 22-34 (2013)

• Sinova, B.; De la Rosa de Saa, S.; Lubiano, M.A.; Gil, M.A.: An overview on the statistical central tendency for fuzzy datasets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 23 (Suppl. 1), 105-132 (2015)

• 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 200, 99-115 (2012)

• Sinova, B.; Gil, M.A.; Lopez, M.T.; Van Aelst, S.: A parameterized L2 metric between fuzzy numbers and its parameter interpretation, Fuzzy Sets and Systems 245, 101-115 (2014)

• Sinova, B.; Gil, M.A.; Van Aelst, S.: M-estimates of location for the robust central tendency of fuzzy data, IEEE Transactions on Fuzzy Systems 24(4), 945-956 (2016)

See Also

https://bellman.ciencias.uniovi.es/smire+codire/FuzzyStatTraRpackage.html

Description

A 'FuzzyNumber' is an array of dimension nl x 3 x 1. It must be valid.

Methods

Public methods

• FuzzyNumber$new()

• FuzzyNumber$getAlphaLevels()

• FuzzyNumber$getInfimums()

• FuzzyNumber$getSupremums()

• FuzzyNumber$plot()

• FuzzyNumber$clone()

Method new()

This method creates a valid 'FuzzyNumber' object with all its attributes set.

Usage

FuzzyNumber$new(fnLevels = NA)

Arguments

Details

See examples.

Returns

The FuzzyNumber object created with all its attributes set if it is valid.

Examples

# Example 1:
FuzzyNumber$new(array(c(0.0,0.5,1.0,-1.5,-1.0,-1.0,2.0,1.5,1.0),dim=c(3,3)))

# Example 2:
FuzzyNumber$new(array(c(0.0,1.0,1,2,4,3),dim=c(2,3)))

Method getAlphaLevels()

This method gives the 'alphaLevels' array of the 'FuzzyNumber'.

Usage

FuzzyNumber$getAlphaLevels()

Details

See examples.

Returns

The array alphaLevels of the FuzzyNumber object.

Examples

FuzzyNumber$new(array(c(0.0,0.5,1.0,-1.5,-1.0,-1.0,2.0,1.5,1.0),dim=c(3,3))
)$getAlphaLevels()

Method getInfimums()

This method gives the 'imfimums' array of the 'FuzzyNumber'.

Usage

FuzzyNumber$getInfimums()

Details

See examples.

Returns

The array imfimums of the FuzzyNumber object.

Examples

FuzzyNumber$new(array(c(0.0,0.5,1.0,-1.5,-1.0,-1.0,2.0,1.5,1.0),dim=c(3,3))
)$getInfimums()

Method getSupremums()

This method gives the 'supremums' array of the 'FuzzyNumber'.

Usage

FuzzyNumber$getSupremums()

Details

See examples.

Returns

The array supremums of the FuzzyNumber object.

Examples

FuzzyNumber$new(array(c(0.0,0.5,1.0,-1.5,-1.0,-1.0,2.0,1.5,1.0),dim=c(3,3))
)$getSupremums()

Method plot()

This method shows in a graph the values of the alphaLevels, infimums and supremums attributes of the corresponding 'FuzzyNumber'.

Usage

FuzzyNumber$plot(color = "grey")

Arguments

Details

See examples.

Returns

a graph with the values of the alphaLevels, infimums and supremums attributes of the corresponding 'FuzzyNumber'.

Examples

# Example 1:
FuzzyNumber$new(array(c(0.0,0.5,1.0,-1.5,-1.0,-1.0,2.0,1.5,1.0),dim=c(3,3))
)$plot()

# Example 2:
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 2, 1.7),dim=c(2,3))
)$plot("blue")

# Example 3:
Simulation$new()$simulCase1(1L)$transfTra()$getDimension(1L)$plot(palette())

# Example 4:
Simulation$new()$simulCase1(1L)$transfTra()$getDimension(1L)$plot(palette()[7])

Method clone()

The objects of this class are cloneable with this method.

Usage

FuzzyNumber$clone(deep = FALSE)

Arguments

Note

In case you find (almost surely existing) bugs or have recommendations for improving the method, comments are welcome to the above mentioned mail addresses.

Author(s)

Andrea Garcia Cernuda <[email protected]>

Examples

## ------------------------------------------------
## Method `FuzzyNumber$new`
## ------------------------------------------------

# Example 1:
FuzzyNumber$new(array(c(0.0,0.5,1.0,-1.5,-1.0,-1.0,2.0,1.5,1.0),dim=c(3,3)))

# Example 2:
FuzzyNumber$new(array(c(0.0,1.0,1,2,4,3),dim=c(2,3)))

## ------------------------------------------------
## Method `FuzzyNumber$getAlphaLevels`
## ------------------------------------------------

FuzzyNumber$new(array(c(0.0,0.5,1.0,-1.5,-1.0,-1.0,2.0,1.5,1.0),dim=c(3,3))
)$getAlphaLevels()

## ------------------------------------------------
## Method `FuzzyNumber$getInfimums`
## ------------------------------------------------

FuzzyNumber$new(array(c(0.0,0.5,1.0,-1.5,-1.0,-1.0,2.0,1.5,1.0),dim=c(3,3))
)$getInfimums()

## ------------------------------------------------
## Method `FuzzyNumber$getSupremums`
## ------------------------------------------------

FuzzyNumber$new(array(c(0.0,0.5,1.0,-1.5,-1.0,-1.0,2.0,1.5,1.0),dim=c(3,3))
)$getSupremums()

## ------------------------------------------------
## Method `FuzzyNumber$plot`
## ------------------------------------------------

# Example 1:
FuzzyNumber$new(array(c(0.0,0.5,1.0,-1.5,-1.0,-1.0,2.0,1.5,1.0),dim=c(3,3))
)$plot()

# Example 2:
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 2, 1.7),dim=c(2,3))
)$plot("blue")

# Example 3:
Simulation$new()$simulCase1(1L)$transfTra()$getDimension(1L)$plot(palette())

# Example 4:
Simulation$new()$simulCase1(1L)$transfTra()$getDimension(1L)$plot(palette()[7])

Description

'FuzzyNumberList' must contain valid 'FuzzyNumbers'. This class implements a version of the empty 'StatList' methods.

Super class

FuzzyStatTraEOO::StatList -> FuzzyNumberList

Methods

Public methods

• FuzzyNumberList$new()

• FuzzyNumberList$dthetaphi()

• FuzzyNumberList$dwablphi()

• FuzzyNumberList$rho1()

• FuzzyNumberList$addFuzzyNumber()

• FuzzyNumberList$removeFuzzyNumber()

• FuzzyNumberList$getDimension()

• FuzzyNumberList$plot()

• FuzzyNumberList$getLength()

• FuzzyNumberList$clone()

Method new()

This method creates a 'FuzzyNumberList' object with the columns and dimensions attributes set where the 'FuzzyNumbers' must be valid.

Usage

FuzzyNumberList$new(numbers = NA)

Arguments

Details

See examples.

Returns

The FuzzyNumberList object created with the columns and dimensions attributes set where the 'FuzzyNumbers' must be valid.

Examples

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.0,-1.0, 2.0, 1.5, 1.0), dim =
c(3, 3))), FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0, 3.0, 2.0,
1.0), dim = c(3, 3)))))

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2.0, 1.5), dim = c(2, 3)))))

Method dthetaphi()

This method calculates the mid/spr distance between the FuzzyNumbers contained in the current object and the one passed as parameter. See Blanco-Fernandez et al. (2013) [1].

Usage

FuzzyNumberList$dthetaphi(s = NA, a = 1, b = 1, theta = 1)

Arguments

Details

See examples.

Returns

a matrix containing the mid/spr distances between the two previous mentioned FuzzyNumberLists. If the body's method inner conditions are not met, NA will be returned.

Examples

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.0, -1.0, 1.5, 1.0), dim = c(2, 3)))
))$dthetaphi(
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -0.5, 0, 1.5, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 1.5, 1.5), dim = c(2, 3))))),
1,5,1)

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.0, -1.0, 2.0, 1.5, 1.0), dim =
c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.25, -1.0, 3.0, 2.0,
1.0), dim = c(3, 3))), FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0, 1.0, 1.0, 2.5,
2.0, 1.5), dim = c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0.5 , 1, 1.5,
3, 2.0, 2), dim = c(3, 3)))))$dthetaphi(FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,1,1.25,1.5, 2, 1.75, 1.5), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1,-0.5,0, 1.5, 1.25, 1), dim = c(3, 3))))
), 1, 1, 1/3)

# Example 3:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(20L)
F=F$transfTra()
S=S$transfTra()
F$dthetaphi(S,1,5,1)

# Example 4:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(10L)
F$dthetaphi(S,2,1,1/3)

# Example 5:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(10L)
F=F$transfTra()
S=S$transfTra(50L)
F$dthetaphi(S,2,1,1)

Method dwablphi()

This method calculates the ($\phi$,$\theta$)-wabl/ldev/rdev distance between the 'FuzzyNumbers' contained in two 'FuzzyNumberLists'. The method checks if the $\alpha$-levels of all 'FuzzyNumbers' coincide. See Sinova et al. (2013) [3] and Sinova et al. (2016) [4].

Usage

FuzzyNumberList$dwablphi(s = NA, a = 1, b = 1, theta = 1)

Arguments

Details

See examples.

Returns

a matrix containing the ($\phi$,$\theta$)-wabl/ldev/rdev distances between the two previous mentioned FuzzyNumberLists. If the body's method inner conditions are not met, NA will be returned.

Examples

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.0, -1.0, 1.5, 1.0), dim = c(2, 3)))
))$dwablphi(
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -0.5, 0, 1.5, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 1.5, 1.5), dim = c(2, 3))))),
1,5,1)

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.0, -1.0, 2.0, 1.5, 1.0), dim =
c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.25, -1.0, 3.0, 2.0,
1.0), dim = c(3, 3))), FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0, 1.0, 1.0, 2.5,
2.0, 1.5), dim = c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0.5 , 1, 1.5,
3, 2.0, 2), dim = c(3, 3)))))$dwablphi(FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,1,1.25,1.5, 2, 1.75, 1.5), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1,-0.5,0, 1.5, 1.25, 1), dim = c(3, 3))))
), 1, 1, 1/3)

# Example 3:
F=Simulation$new()$simulCase1(3L)
S=Simulation$new()$simulCase1(4L)
F=F$transfTra()
S=S$transfTra()
F$dwablphi(S,2,1,1)

# Example 4:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(10L)
F$dwablphi(S)

# Example 5:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(10L)
F=F$transfTra()
S=S$transfTra(50L)
F$dwablphi(S,2,1,1)

Method rho1()

This method calculates the 1-norm distance between the 'FuzzyNumbers' contained in two 'FuzzyNumberLists'. The method checks if the $\alpha$-levels of all 'FuzzyNumbers' coincide. See Diamond and Kloeden. (1990) [2].

Usage

FuzzyNumberList$rho1(s = NA)

Arguments

Details

See examples.

Returns

a matrix containing the 1-norm distances between the two previous mentioned FuzzyNumberLists. If the body's method inner conditions are not met, NA will be returned.

Examples

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.0, -1.0, 1.5, 1.0), dim = c(2, 3)))
))$rho1(
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -0.5, 0, 1.5, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 1.5, 1.5), dim = c(2, 3))))))

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.0, -1.0, 2.0, 1.5, 1.0), dim =
c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.25, -1.0, 3.0, 2.0,
1.0), dim = c(3, 3))), FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0, 1.0, 1.0, 2.5,
2.0, 1.5), dim = c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0.5 , 1, 1.5,
3, 2.0, 2), dim = c(3, 3)))))$rho1(FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,1,1.25,1.5, 2, 1.75, 1.5), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1,-0.5,0, 1.5, 1.25, 1), dim = c(3, 3))))))

# Example 3:
F=Simulation$new()$simulCase1(4L)
S=Simulation$new()$simulCase1(5L)
F=F$transfTra()
S=S$transfTra()
F$rho1(S)
S$rho1(F)

# Example 4:
F=Simulation$new()$simulCase1(4L)
S=Simulation$new()$simulCase1(5L)
F=F$transfTra()
S=S$transfTra(10L)
F$rho1(S)
S$rho1(F)

Method addFuzzyNumber()

This method adds a 'FuzzyNumber' to the current collection of fuzzy numbers. Therefore, the dimensions' field is increased in a unit.

Usage

FuzzyNumberList$addFuzzyNumber(n = NA, verbose = TRUE)

Arguments

Details

See examples.

Returns

NULL.

Examples

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3)))))$addFuzzyNumber(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))))

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3)))
))$addFuzzyNumber( FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75,
1.5), dim = c(3, 3))))

Method removeFuzzyNumber()

This method removes a 'FuzzyNumber' to the current collection of fuzzy numbers. Therefore, the dimensions' field is decreased in a unit.

Usage

FuzzyNumberList$removeFuzzyNumber(i = NA, verbose = TRUE)

Arguments

Details

See examples.

Returns

NULL.

Examples

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1, -0.5, 1.5, 1.25), dim = c(2, 3)))
))$removeFuzzyNumber(1L)

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75, 1.5), dim = c(3, 3)))
))$removeFuzzyNumber(2L)

Method getDimension()

This method gives the number contained in the dimension passed as parameter when the dimension is greater than 0 and not greater than the dimensions of the 'FuzzyNumberList's' numbers array.

Usage

FuzzyNumberList$getDimension(i = NA)

Arguments

Details

See examples.

Returns

The FuzzyNumber contained in the dimension passed as parameter or an error if the dimension is not valid.

Examples

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75, 1.5), dim = c(3, 3)))
))$getDimension(1L)

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75, 1.5), dim = c(3, 3)))
))$getDimension(2L)

Method plot()

This method shows in a graph the values of the attribute numbers of the corresponding 'FuzzyNumberList'.

Usage

FuzzyNumberList$plot(color = "grey")

Arguments

Details

See examples.

Returns

a graph with the values of the attribute numbers of the corresponding 'FuzzyNumberList'.

Examples

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75, 1.5), dim = c(3, 3)))
))$plot()

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.0, -1.0, 1.5, 1.0), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -0.5, 0, 1.5, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 1.85, 1.7), dim = c(2, 3))))
)$plot("blue")

# Example 3:
Simulation$new()$simulCase1(8L)$transfTra()$plot(palette())

# Example 4:
Simulation$new()$simulCase1(5L)$transfTra()$plot(palette()[2:6])

Method getLength()

This method returns the number of dimensions that are equivalent to the number of 'FuzzyNumbers' in the corresponding 'FuzzyNumberList'.

Usage

FuzzyNumberList$getLength()

Details

See examples.

Returns

the number of dimensions that are equivalent to the number of 'FuzzyNumbers' in the corresponding 'FuzzyNumberList'.

Examples

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75, 1.5), dim = c(3, 3)))
))$getLength()

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.0, -1.0, 1.5, 1.0), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -0.5, 0, 1.5, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 1.5, 1.5), dim = c(2, 3))))
)$getLength()

Method clone()

The objects of this class are cloneable with this method.

Usage

FuzzyNumberList$clone(deep = FALSE)

Arguments

Note

In case you find (almost surely existing) bugs or have recommendations for improving the method, comments are welcome to the above mentioned mail addresses.

Author(s)

(s) Andrea Garcia Cernuda <[email protected]>, Asun Lubiano <[email protected]>, Sara de la Rosa de Saa

References

[1] Blanco-Fernandez, A.; Casals, R.M.; Colubi, A.; Corral, N.; Garcia-Barzana, M.; Gil, M.A.; Gonzalez-Rodriguez, G.; Lopez, M.T.; Lubiano, M.A.; Montenegro, M.; Ramos-Guajardo, A.B.; de la Rosa de Saa, S.; Sinova, B.: Random fuzzy sets: A mathematical tool to develop statistical fuzzy data analysis, Iranian Journal on Fuzzy Systems 10(2), 1-28 (2013)

[2] Diamond, P.; Kloeden, P.: Metric spaces of fuzzy sets, Fuzzy Sets and Systems 35, 241-249 (1990)

[3] Sinova, B.; de la Rosa de Saa, S.; Gil, M.A.: A generalized L1-type metric between fuzzy numbers for an approach to central tendency of fuzzy data, Information Sciences 242, 22-34 (2013)

[4] Sinova, B.; Gil, M.A.; Van Aelst, S.: M-estimates of location for the robust central tendency of fuzzy data, IEEE Transactions on Fuzzy Systems 24(4), 945-956 (2016)

Examples

## ------------------------------------------------
## Method `FuzzyNumberList$new`
## ------------------------------------------------

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.0,-1.0, 2.0, 1.5, 1.0), dim =
c(3, 3))), FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0, 3.0, 2.0,
1.0), dim = c(3, 3)))))

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2.0, 1.5), dim = c(2, 3)))))

## ------------------------------------------------
## Method `FuzzyNumberList$dthetaphi`
## ------------------------------------------------

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.0, -1.0, 1.5, 1.0), dim = c(2, 3)))
))$dthetaphi(
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -0.5, 0, 1.5, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 1.5, 1.5), dim = c(2, 3))))),
1,5,1)

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.0, -1.0, 2.0, 1.5, 1.0), dim =
c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.25, -1.0, 3.0, 2.0,
1.0), dim = c(3, 3))), FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0, 1.0, 1.0, 2.5,
2.0, 1.5), dim = c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0.5 , 1, 1.5,
3, 2.0, 2), dim = c(3, 3)))))$dthetaphi(FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,1,1.25,1.5, 2, 1.75, 1.5), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1,-0.5,0, 1.5, 1.25, 1), dim = c(3, 3))))
), 1, 1, 1/3)

# Example 3:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(20L)
F=F$transfTra()
S=S$transfTra()
F$dthetaphi(S,1,5,1)

# Example 4:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(10L)
F$dthetaphi(S,2,1,1/3)

# Example 5:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(10L)
F=F$transfTra()
S=S$transfTra(50L)
F$dthetaphi(S,2,1,1)

## ------------------------------------------------
## Method `FuzzyNumberList$dwablphi`
## ------------------------------------------------

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.0, -1.0, 1.5, 1.0), dim = c(2, 3)))
))$dwablphi(
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -0.5, 0, 1.5, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 1.5, 1.5), dim = c(2, 3))))),
1,5,1)

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.0, -1.0, 2.0, 1.5, 1.0), dim =
c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.25, -1.0, 3.0, 2.0,
1.0), dim = c(3, 3))), FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0, 1.0, 1.0, 2.5,
2.0, 1.5), dim = c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0.5 , 1, 1.5,
3, 2.0, 2), dim = c(3, 3)))))$dwablphi(FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,1,1.25,1.5, 2, 1.75, 1.5), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1,-0.5,0, 1.5, 1.25, 1), dim = c(3, 3))))
), 1, 1, 1/3)

# Example 3:
F=Simulation$new()$simulCase1(3L)
S=Simulation$new()$simulCase1(4L)
F=F$transfTra()
S=S$transfTra()
F$dwablphi(S,2,1,1)

# Example 4:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(10L)
F$dwablphi(S)

# Example 5:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(10L)
F=F$transfTra()
S=S$transfTra(50L)
F$dwablphi(S,2,1,1)

## ------------------------------------------------
## Method `FuzzyNumberList$rho1`
## ------------------------------------------------

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.0, -1.0, 1.5, 1.0), dim = c(2, 3)))
))$rho1(
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -0.5, 0, 1.5, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 1.5, 1.5), dim = c(2, 3))))))

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.0, -1.0, 2.0, 1.5, 1.0), dim =
c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1.5, -1.25, -1.0, 3.0, 2.0,
1.0), dim = c(3, 3))), FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0, 1.0, 1.0, 2.5,
2.0, 1.5), dim = c(3, 3))),FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 0.5 , 1, 1.5,
3, 2.0, 2), dim = c(3, 3)))))$rho1(FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,1,1.25,1.5, 2, 1.75, 1.5), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1,-0.5,0, 1.5, 1.25, 1), dim = c(3, 3))))))

# Example 3:
F=Simulation$new()$simulCase1(4L)
S=Simulation$new()$simulCase1(5L)
F=F$transfTra()
S=S$transfTra()
F$rho1(S)
S$rho1(F)

# Example 4:
F=Simulation$new()$simulCase1(4L)
S=Simulation$new()$simulCase1(5L)
F=F$transfTra()
S=S$transfTra(10L)
F$rho1(S)
S$rho1(F)

## ------------------------------------------------
## Method `FuzzyNumberList$addFuzzyNumber`
## ------------------------------------------------

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3)))))$addFuzzyNumber(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))))

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3)))
))$addFuzzyNumber( FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75,
1.5), dim = c(3, 3))))

## ------------------------------------------------
## Method `FuzzyNumberList$removeFuzzyNumber`
## ------------------------------------------------

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1, -0.5, 1.5, 1.25), dim = c(2, 3)))
))$removeFuzzyNumber(1L)

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75, 1.5), dim = c(3, 3)))
))$removeFuzzyNumber(2L)

## ------------------------------------------------
## Method `FuzzyNumberList$getDimension`
## ------------------------------------------------

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75, 1.5), dim = c(3, 3)))
))$getDimension(1L)

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75, 1.5), dim = c(3, 3)))
))$getDimension(2L)

## ------------------------------------------------
## Method `FuzzyNumberList$plot`
## ------------------------------------------------

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75, 1.5), dim = c(3, 3)))
))$plot()

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.0, -1.0, 1.5, 1.0), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -0.5, 0, 1.5, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 1.85, 1.7), dim = c(2, 3))))
)$plot("blue")

# Example 3:
Simulation$new()$simulCase1(8L)$transfTra()$plot(palette())

# Example 4:
Simulation$new()$simulCase1(5L)$transfTra()$plot(palette()[2:6])

## ------------------------------------------------
## Method `FuzzyNumberList$getLength`
## ------------------------------------------------

# Example 1:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, -1, -0.5, 0, 1.5, 1.25, 1), dim = c(3, 3))),
FuzzyNumber$new(array(c(0.0, 0.5, 1.0, 1, 1.25, 1.5, 2, 1.75, 1.5), dim = c(3, 3)))
))$getLength()

# Example 2:
FuzzyNumberList$new(c(
FuzzyNumber$new(array(c(0.0, 1.0, -1.5, -1.0, 2, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -1.0, -1.0, 1.5, 1.0), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, -0.5, 0, 1.5, 1), dim = c(2, 3))),
FuzzyNumber$new(array(c(0.0, 1.0, 1, 1.5, 1.5, 1.5), dim = c(2, 3))))
)$getLength()

Description

A dataset containing 69 trapezoidal fuzzy numbers. The data correspond to the well-knows questionaire TIMSS-PIRLS2011. This questionnaire was adapted to allow a double-type response, namely, the original Likert and a fuzzy rating scale-based (to simplify, trapezoidal). The questionnaire was conducted on 69 fourth grade students from Colegio San Ignacio (Oviedo-Asturias, Spain). Trapezoidal fuzzy rating responses to the Question M1 "I like mathematics" are collected in this dataset.

Usage

M1

Format

A matrix with 69 rows and 4 columns:

inf0

infimum of support of the trapezoidal fuzzy numbers, real number

inf1

infimum of core of the trapezoidal fuzzy numbers, real number

sup1

supremum of core of the trapezoidal fuzzy numbers, real number

sup0

supremum of support of the trapezoidal fuzzy numbers, real number

Source

http://bellman.ciencias.uniovi.es/SMIRE/FuzzyRatingScaleQuestionnaire-SanIgnacio.html

References

[1] Gil, M.A.; Lubiano, M.A.; De la Rosa de Saa, S.; Sinova, B.: Analyzing data from a fuzzy rating scale-based questionnaire. A case study, Psicothema 27(2), 182-191 (2015)

[2] Lubiano, M.A.; De la Rosa de Saa, S.; Montenegro, M.; Sinova, B.; Gil, M.A.: Descriptive analysis of responses to items in questionnaires. Why not a fuzzy rating scale?, Information Sciences 360, 131-148 (2016)

[3] Lubiano, M.A.; Salas, A.; Carleos, C.; De la Rosa de Sáa, S.; Gil, M.Á.: Hypothesis testing-based comparative analysis between rating scales for intrinsically imprecise data, International Journal of Approximate Reasoning 88, 128-147 (2017)

Examples

M1

Description

A dataset containing 69 trapezoidal fuzzy numbers. The data correspond to the well-knows questionaire TIMSS-PIRLS2011. This questionnaire was adapted to allow a double-type response, namely, the original Likert and a fuzzy rating scale-based (to simplify, trapezoidal). The questionnaire was conducted on 69 fourth grade students from Colegio San Ignacio (Oviedo-Asturias, Spain). Trapezoidal fuzzy rating responses to the Question M2 "My teacher is easy to understand" are collected in this dataset.

Usage

M2

Format

A matrix with 69 rows and 4 columns:

inf0

infimum of support of the trapezoidal fuzzy numbers, real number

inf1

infimum of core of the trapezoidal fuzzy numbers, real number

sup1

supremum of core of the trapezoidal fuzzy numbers, real number

sup0

supremum of support of the trapezoidal fuzzy numbers, real number

Source

http://bellman.ciencias.uniovi.es/SMIRE/FuzzyRatingScaleQuestionnaire-SanIgnacio.html

References

[1] Gil, M.A.; Lubiano, M.A.; De la Rosa de Saa, S.; Sinova, B.: Analyzing data from a fuzzy rating scale-based questionnaire. A case study, Psicothema 27(2), 182-191 (2015)

[2] Lubiano, M.A.; De la Rosa de Saa, S.; Montenegro, M.; Sinova, B.; Gil, M.A.: Descriptive analysis of responses to items in questionnaires. Why not a fuzzy rating scale?, Information Sciences 360, 131-148 (2016)

[3] Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications, European Journal of Operational Research 251, 918-929 (2016)

[3] Lubiano, M.A.; Salas, A.; Carleos, C.; De la Rosa de Sáa, S.; Gil, M.Á.: Hypothesis testing-based comparative analysis between rating scales for intrinsically imprecise data, International Journal of Approximate Reasoning 88, 128-147 (2017)

[4] Lubiano, M.A.; Salas, A.; Gil, M.Á.: A hypothesis testing-based discussion on the sensitivity of means of Fuzzy data with respect to data shape, Fuzzy Sets and Systems 328(1), 54-69 (2017)

Examples

M2

Description

A dataset containing 69 trapezoidal fuzzy numbers. The data correspond to the well-knows questionaire TIMSS-PIRLS2011. This questionnaire was adapted to allow a double-type response, namely, the original Likert and a fuzzy rating scale-based (to simplify, trapezoidal). The questionnaire was conducted on 69 fourth grade students from Colegio San Ignacio (Oviedo-Asturias, Spain). Trapezoidal fuzzy rating responses to the Question M3 "Mathematics is harder for me than any other subject" are collected in this dataset.

Usage

M3

Format

A matrix with 69 rows and 4 columns:

inf0

infimum of support of the trapezoidal fuzzy numbers, real number

inf1

infimum of core of the trapezoidal fuzzy numbers, real number

sup1

supremum of core of the trapezoidal fuzzy numbers, real number

sup0

supremum of support of the trapezoidal fuzzy numbers, real number

Source

http://bellman.ciencias.uniovi.es/SMIRE/FuzzyRatingScaleQuestionnaire-SanIgnacio.html

References

[1] Gil, M.A.; Lubiano, M.A.; De la Rosa de Saa, S.; Sinova, B.: Analyzing data from a fuzzy rating scale-based questionnaire. A case study, Psicothema 27(2), 182-191 (2015)

[2] Lubiano, M.A.; De la Rosa de Saa, S.; Montenegro, M.; Sinova, B.; Gil, M.A.: Descriptive analysis of responses to items in questionnaires. Why not a fuzzy rating scale?, Information Sciences 360, 131-148 (2016)

[3] Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications, European Journal of Operational Research 251, 918-929 (2016)

[4] Lubiano, M.A.; Salas, A.; Carleos, C.; De la Rosa de Sáa, S.; Gil, M.Á.: Hypothesis testing-based comparative analysis between rating scales for intrinsically imprecise data, International Journal of Approximate Reasoning 88, 128-147 (2017)

Examples

M3

Description

A dataset containing 69 trapezoidal fuzzy numbers. The data correspond to the well-knows questionaire TIMSS-PIRLS2011. This questionnaire was adapted to allow a double-type response, namely, the original Likert and a fuzzy rating scale-based (to simplify, trapezoidal). The questionnaire was conducted on 69 fourth grade students from Colegio San Ignacio (Oviedo-Asturias, Spain). Trapezoidal fuzzy rating responses to the Question S1 "My teacher taught me to discover science in daily life" are collected in this dataset.

Usage

S1

Format

A matrix with 69 rows and 4 columns:

inf0

infimum of support of the trapezoidal fuzzy numbers, real number

inf1

infimum of core of the trapezoidal fuzzy numbers, real number

sup1

supremum of core of the trapezoidal fuzzy numbers, real number

sup0

supremum of support of the trapezoidal fuzzy numbers, real number

Source

http://bellman.ciencias.uniovi.es/SMIRE/FuzzyRatingScaleQuestionnaire-SanIgnacio.html

References

[1] Gil, M.A.; Lubiano, M.A.; De la Rosa de Saa, S.; Sinova, B.: Analyzing data from a fuzzy rating scale-based questionnaire. A case study, Psicothema 27(2), 182-191 (2015)

[2] Lubiano, M.A.; De la Rosa de Saa, S.; Montenegro, M.; Sinova, B.; Gil, M.A.: Descriptive analysis of responses to items in questionnaires. Why not a fuzzy rating scale?, Information Sciences 360, 131-148 (2016)

[3] Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications, European Journal of Operational Research 251, 918-929 (2016)

[4] Lubiano, M.A.; Salas, A.; Carleos, C.; De la Rosa de Sáa, S.; Gil, M.Á.: Hypothesis testing-based comparative analysis between rating scales for intrinsically imprecise data, International Journal of Approximate Reasoning 88, 128-147 (2017)

[5] Lubiano, M.A.; Salas, A.; Gil, M.Á.: A hypothesis testing-based discussion on the sensitivity of means of Fuzzy data with respect to data shape, Fuzzy Sets and Systems 328(1), 54-69 (2017)

Examples

S1

Description

Simulation contains 5 different methods that gives the user a 'TrapezoidalFuzzyNumberList'.

Methods

Public methods

• Simulation$simulCase1()

• Simulation$simulCase2()

• Simulation$simulCase3()

• Simulation$simulCase4()

• Simulation$simulFRSTra()

• Simulation$clone()

Method simulCase1()

This method generates n 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList' from a symmetric distribution and with independent components (for a detailed explanation of the simulation see Sinova et al. (2012) [3], namely, the Case 1 for noncontaminated samples).

Usage

Simulation$simulCase1(n = NA)

Arguments

Details

See examples.

Returns

a TrapezoidalFuzzyNumberList with n TrapezoidalFuzzyNumbers. Each one is characterized by its four values inf0, inf1, sup1, sup0.

Examples

Simulation$new()$simulCase1(10L)

Method simulCase2()

This method generates n 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList' from a symmetric distribution and with dependent components (for a detailed explanation of the simulation see Sinova et al. (2012) [3], namely, the Case 2 for noncontaminated samples).

Usage

Simulation$simulCase2(n = NA)

Arguments

Details

See examples.

Returns

a TrapezoidalFuzzyNumberList with n TrapezoidalFuzzyNumbers. Each one is characterized by its four values inf0, inf1, sup1, sup0.

Examples

Simulation$new()$simulCase2(10L)

Method simulCase3()

This method generates n 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList' from a asymmetric distribution and with independent components (for a detailed explanation of the simulation see Sinova et al. (2012) [4], namely, the Case 3 for noncontaminated samples).

Usage

Simulation$simulCase3(n = NA)

Arguments

Details

See examples.

Returns

a TrapezoidalFuzzyNumberList with n TrapezoidalFuzzyNumbers. Each one is characterized by its four values inf0, inf1, sup1, sup0.

Examples

Simulation$new()$simulCase3(10L)

Method simulCase4()

This method generates n 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList' from a asymmetric distribution and with dependent components (for a detailed explanation of the simulation see Sinova et al. (2012) [4], namely, the Case 4 for noncontaminated samples).

Usage

Simulation$simulCase4(n = NA)

Arguments

Details

See examples.

Returns

a TrapezoidalFuzzyNumberList with n TrapezoidalFuzzyNumbers. Each one is characterized by its four values inf0, inf1, sup1, sup0.

Examples

Simulation$new()$simulCase4(10L)

Method simulFRSTra()

This method generates n 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList' based on the fuzzy rating scale. They are simulated mimicking the human behavior, considering for it a finite mixture of three different procedures (for a detailed explanation of the simulation see De la Rosa de Saa et al. (2012) [1]), and generated in the interval [0,1].

Usage

Simulation$simulFRSTra(n = NA, w1 = NA, w2 = NA, w3 = NA, p = NA, q = NA)

Arguments

Details

See examples.

Returns

a TrapezoidalFuzzyNumberList with n TrapezoidalFuzzyNumbers with values in the interval [0,1]. Each trapezoidal fuzzy rating response is characterized by its four values inf0, inf1, sup1, sup0.

Examples

Simulation$new()$simulFRSTra(100L,0.05,0.35,0.6,2,1)

Method clone()

The objects of this class are cloneable with this method.

Usage

Simulation$clone(deep = FALSE)

Arguments

Note

In case you find (almost surely existing) bugs or have recommendations for improving the method comments are welcome to the below mentioned mail addresses.

Author(s)

(s) Andrea Garcia Cernuda <[email protected]>, Asun Lubiano <[email protected]>, Sara de la Rosa de Saa

References

[1] De la Rosa de Saa, S.; Gil, M.A.; Gonzalez-Rodriguez, G.; Lopez, M.T.; Lubiano M.A.: Fuzzy rating scale-based questionnaires and their statistical analysis, IEEE Transactions on Fuzzy Systems 23(1), 111-126 (2015)

[2] Lubiano, M.A.; Salas, A.; Carleos, C.; De la Rosa de Sáa, S.; Gil, M.Á.: Hypothesis testing-based comparative analysis between rating scales for intrinsically imprecise data, International Journal of Approximate Reasoning 88, 128-147 (2017)

[3] 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 200, 99-115 (2012)

[4] Sinova, B.; Gil, M.A.; Van Aelst, S.: M-estimates of location for the robust central tendency of fuzzy data, IEEE Transactions on Fuzzy Systems 24(4), 945-956 (2016)

Examples

## ------------------------------------------------
## Method `Simulation$simulCase1`
## ------------------------------------------------

Simulation$new()$simulCase1(10L)

## ------------------------------------------------
## Method `Simulation$simulCase2`
## ------------------------------------------------

Simulation$new()$simulCase2(10L)

## ------------------------------------------------
## Method `Simulation$simulCase3`
## ------------------------------------------------

Simulation$new()$simulCase3(10L)

## ------------------------------------------------
## Method `Simulation$simulCase4`
## ------------------------------------------------

Simulation$new()$simulCase4(10L)

## ------------------------------------------------
## Method `Simulation$simulFRSTra`
## ------------------------------------------------

Simulation$new()$simulFRSTra(100L,0.05,0.35,0.6,2,1)

Description

'StatList' defines the common attributes and methods of 'FuzzyNumberList' and 'TrapezoidalFuzzyNumberList'. All methods are empty except for some attribute checking, the child classes are the ones that have to give the implementation for the empty methods.

Methods

Public methods

• StatList$new()

• StatList$dthetaphi()

• StatList$dwablphi()

• StatList$rho1()

• StatList$plot()

• StatList$getLength()

• StatList$clone()

Method new()

This method warns the user that this class can not be initialized as it is abstract.

Usage

StatList$new()

Returns

shows a message telling that this class can not be initialized.

Method dthetaphi()

This method calculates the mid/spr distance between the numbers contain in two 'StatLists'.

Usage

StatList$dthetaphi(s = NA, a = 1, b = 1, theta = 1)

Arguments

Returns

a matrix containing the mid/spr distances between the two previous mentioned StatLists.

Method dwablphi()

This method calculates the ($\phi$,$\theta$)-wabl/ldev/rdev distance between the numbers contained in two 'StatLists'.

Usage

StatList$dwablphi(s = NA, a = 1, b = 1, theta = 1)

Arguments

Returns

a StatList containing the ($\phi$,$\theta$)-wabl/ldev/rdev distances between the two previous mentioned StatLists.

Method rho1()

This method calculates the 1-norm distance between the numbers contained in two 'StatLists'.

Usage

StatList$rho1(s = NA)

Arguments

Returns

a StatList containing the 1-norm distances between the two previous mentioned StatLists.

Method plot()

This method shows in a graph the inner numbers of the corresponding 'StatList'.

Usage

StatList$plot(color = "grey")

Arguments

Returns

a graph with the inner numbers of the corresponding 'StatList' represented.

Method getLength()

This method returns the number of dimensions that are equivalent to the number of numbers in the corresponding 'StatList'.

Usage

StatList$getLength()

Returns

the number of dimensions that are equivalent to the number of numbers in the corresponding 'StatList'.

Method clone()

The objects of this class are cloneable with this method.

Usage

StatList$clone(deep = FALSE)

Arguments

Note

In order to have the documentation completed, we had had to write the documentation of this class. Taking into account that this class is part of the software design and it cannot be initialized, all its documentation is not needed, in particular the new and clone methods, apart from the Usage: section of each method documentation. All its methods can be used and can be found in FuzzyNumberList's and TrapezoidalFuzzyNumberList's documentation.

We are working to improve this issue. In case you find (almost surely existing) bugs or have recommendations for improving the method, comments are welcome to the above mentioned mail addresses.

Author(s)

Andrea Garcia Cernuda <[email protected]>

Description

A 'TrapezoidalFuzzyNumber' is characterized by their four values inf0, inf1, sup1 and sup0. Its' values are checked in order to only provide a valid 'TrapezoidalFuzzyNumber'.

Methods

Public methods

• TrapezoidalFuzzyNumber$new()

• TrapezoidalFuzzyNumber$getInf0()

• TrapezoidalFuzzyNumber$getInf1()

• TrapezoidalFuzzyNumber$getSup1()

• TrapezoidalFuzzyNumber$getSup0()

• TrapezoidalFuzzyNumber$is_positive()

• TrapezoidalFuzzyNumber$plot()

• TrapezoidalFuzzyNumber$clone()

Method new()

This method creates a valid 'TrapezoidalFuzzyNumber' object with all its attributes set.

Usage

TrapezoidalFuzzyNumber$new(inf0 = NA, inf1 = NA, sup1 = NA, sup0 = NA)

Arguments

Details

See examples.

Returns

The TrapezoidalFuzzyNumber object created with all its attributes set if it is valid.

Examples

# Example 1:
TrapezoidalFuzzyNumber$new(1,2,3,4)

# Example 2:
TrapezoidalFuzzyNumber$new(-8,-6,-4,-2)

# Example 3:
TrapezoidalFuzzyNumber$new(-1,-1,2,3)

# Example 4:
TrapezoidalFuzzyNumber$new(1,2,3,3)

Method getInf0()

This method gives the inf0 attribute of the 'TrapezoidalFuzzyNumber'.

Usage

TrapezoidalFuzzyNumber$getInf0()

Details

See examples.

Returns

The inf0 attribute of the TrapezoidalFuzzyNumber object.

Examples

TrapezoidalFuzzyNumber$new(1,2,3,4)$getInf0()

Method getInf1()

This method gives the inf1 attribute of the 'TrapezoidalFuzzyNumber'.

Usage

TrapezoidalFuzzyNumber$getInf1()

Details

See examples.

Returns

The inf1 attribute of the TrapezoidalFuzzyNumber object.

Examples

TrapezoidalFuzzyNumber$new(1,2,3,4)$getInf1()

Method getSup1()

This method gives the sup1 attribute of the 'TrapezoidalFuzzyNumber'.

Usage

TrapezoidalFuzzyNumber$getSup1()

Details

See examples.

Returns

The sup1 attribute of the TrapezoidalFuzzyNumber object.

Examples

TrapezoidalFuzzyNumber$new(1,2,3,4)$getSup1()

Method getSup0()

This method gives the sup0 attribute of the 'TrapezoidalFuzzyNumber'.

Usage

TrapezoidalFuzzyNumber$getSup0()

Details

See examples.

Returns

The sup0 attribute of the TrapezoidalFuzzyNumber object.

Examples

TrapezoidalFuzzyNumber$new(1,2,3,4)$getSup0()

Method is_positive()

This method gives information whether the 'TrapezoidalFuzzyNumber' is positive regarding its attributes.

Usage

TrapezoidalFuzzyNumber$is_positive()

Details

See examples.

Returns

TRUE whether the TrapezoidalFuzzyNumber object has all its attributes greater than -1, otherwise FALSE.

Examples

# Example 1:
TrapezoidalFuzzyNumber$new(1,2,3,4)$is_positive()

# Example 2:
TrapezoidalFuzzyNumber$new(-8,-6,-4,-2)$is_positive()

Method plot()

This method shows in a graph the values of the corresponding 'TrapezoidalFuzzyNumber'.

Usage

TrapezoidalFuzzyNumber$plot(color = "grey")

Arguments

Details

See examples.

Returns

a graph with the values of the corresponding 'TrapezoidalFuzzyNumber'.

Examples

# Example 1:
TrapezoidalFuzzyNumber$new(1,2,3,4)$plot()

# Example 2:
TrapezoidalFuzzyNumber$new(-8,-6,-4,-2)$plot("blue")

# Example 3:
TrapezoidalFuzzyNumber$new(0,0,0.5,3)$plot(palette())

# Example 4:
TrapezoidalFuzzyNumber$new(-8,-3.55,0,10)$plot(palette()[5])

Method clone()

The objects of this class are cloneable with this method.

Usage

TrapezoidalFuzzyNumber$clone(deep = FALSE)

Arguments

Note

In case you find (almost surely existing) bugs or have recommendations for improving the method, comments are welcome to the above mentioned mail addresses.

Author(s)

Andrea Garcia Cernuda <[email protected]>

Examples

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumber$new`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumber$new(1,2,3,4)

# Example 2:
TrapezoidalFuzzyNumber$new(-8,-6,-4,-2)

# Example 3:
TrapezoidalFuzzyNumber$new(-1,-1,2,3)

# Example 4:
TrapezoidalFuzzyNumber$new(1,2,3,3)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumber$getInf0`
## ------------------------------------------------

TrapezoidalFuzzyNumber$new(1,2,3,4)$getInf0()

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumber$getInf1`
## ------------------------------------------------

TrapezoidalFuzzyNumber$new(1,2,3,4)$getInf1()

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumber$getSup1`
## ------------------------------------------------

TrapezoidalFuzzyNumber$new(1,2,3,4)$getSup1()

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumber$getSup0`
## ------------------------------------------------

TrapezoidalFuzzyNumber$new(1,2,3,4)$getSup0()

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumber$is_positive`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumber$new(1,2,3,4)$is_positive()

# Example 2:
TrapezoidalFuzzyNumber$new(-8,-6,-4,-2)$is_positive()

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumber$plot`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumber$new(1,2,3,4)$plot()

# Example 2:
TrapezoidalFuzzyNumber$new(-8,-6,-4,-2)$plot("blue")

# Example 3:
TrapezoidalFuzzyNumber$new(0,0,0.5,3)$plot(palette())

# Example 4:
TrapezoidalFuzzyNumber$new(-8,-3.55,0,10)$plot(palette()[5])

Description

'TrapezoidalFuzzyNumberList' must contain valid 'TrapezoidalFuzzyNumbers'. This class implements a version of the empty 'StatList' methods.

Super class

FuzzyStatTraEOO::StatList -> TrapezoidalFuzzyNumberList

Methods

Public methods

• TrapezoidalFuzzyNumberList$new()

• TrapezoidalFuzzyNumberList$add()

• TrapezoidalFuzzyNumberList$dthetaphi()

• TrapezoidalFuzzyNumberList$dwablphi()

• TrapezoidalFuzzyNumberList$gsi()

• TrapezoidalFuzzyNumberList$hyperI()

• TrapezoidalFuzzyNumberList$mEstimator()

• TrapezoidalFuzzyNumberList$mdd()

• TrapezoidalFuzzyNumberList$mean()

• TrapezoidalFuzzyNumberList$median1Norm()

• TrapezoidalFuzzyNumberList$medianWabl()

• TrapezoidalFuzzyNumberList$qn()

• TrapezoidalFuzzyNumberList$rho1()

• TrapezoidalFuzzyNumberList$sn()

• TrapezoidalFuzzyNumberList$tn()

• TrapezoidalFuzzyNumberList$transfTra()

• TrapezoidalFuzzyNumberList$var()

• TrapezoidalFuzzyNumberList$wablphi()

• TrapezoidalFuzzyNumberList$addTrapezoidalFuzzyNumber()

• TrapezoidalFuzzyNumberList$removeTrapezoidalFuzzyNumber()

• TrapezoidalFuzzyNumberList$getDimension()

• TrapezoidalFuzzyNumberList$plot()

• TrapezoidalFuzzyNumberList$getLength()

• TrapezoidalFuzzyNumberList$clone()

Method new()

This method creates a 'TrapezoidalFuzzyNumberList' object with all the attributes set if the 'TrapezoidalFuzzyNumbers' are valid.

Usage

TrapezoidalFuzzyNumberList$new(numbers = NA)

Arguments

Details

See examples.

Returns

The TrapezoidalFuzzyNumberList object created with all attributes set if the 'TrapezoidalFuzzyNumbers' are valid.

Examples

TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1, 2, 3, 4),
TrapezoidalFuzzyNumber$new(-8, -6, -4, -2),
TrapezoidalFuzzyNumber$new(-1, -1, 2, 3),
TrapezoidalFuzzyNumber$new(1, 2, 3, 3)))

Method add()

This method calculates the scale measure Average Distance Deviation (ADD) of a 'TrapezoidalFuzzyNumberList' with respect to a 'TrapezoidalFuzzyNumberList' or with respect to a 'FuzzyNumberList' containing a unique valid fuzzy number. The employed metric in the calculation can be the 1-norm distance, the mid/spr distance or the ($\phi$,$\theta$)-wabl/ldev/rdev distance. See De la Rosa de Saa et al. (2017) [2].

Usage

TrapezoidalFuzzyNumberList$add(s = NA, type = NA, a = 1, b = 1, theta = 1)

Arguments

Details

See examples.

Returns

the scale measure ADD, which is a real number. If the body's method inner conditions are not met, NA will be returned.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
3.0, 2.0, 1.0), dim = c(3, 3))))),1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
3.0, 2.0, 1.0), dim = c(3, 3))))),2L,2,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(5,6,7,8))),3L,1,1,1)

# Example 4:
F=Simulation$new()$simulCase1(10L)
S=F$mean()
F$add(S,1L)

# Example 5:
F=Simulation$new()$simulCase1(100L)
S=F$median1Norm()
F$add(S,2L,2,1,1)

# Example 6:
F=Simulation$new()$simulCase2(10L)
U=Simulation$new()$simulCase2(1L)
F$add(U,2L)

# Example 7:
F=Simulation$new()$simulCase2(10L)
U=F$transfTra()
F$add(U,2L)

# Example 8:
F=Simulation$new()$simulCase2(10L)
U=Simulation$new()$simulCase2(2L)
F$add(U,2L)

Method dthetaphi()

This method calculates the mid/spr distance between the 'TrapezoidalFuzzyNumbers' contained in the current object and the one passed as parameter. See Lubiano et al. (2016) [5].

Usage

TrapezoidalFuzzyNumberList$dthetaphi(s = NA, a = 1, b = 1, theta = 1)

Arguments

Details

See examples.

Returns

a matrix containing the mid/spr distances between the two previous mentioned TrapezoidalFuzzyNumberLists.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dthetaphi(
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dthetaphi(
TrapezoidalFuzzyNumberList$new( c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))),1,1,1)

# Example 3:
F=Simulation$new()$simulCase1(6L)
S=Simulation$new()$simulCase1(8L)
F$dthetaphi(S,1,5,1)

Method dwablphi()

This method calculates the ($\phi$,$\theta$)-wabl/ldev/rdev distance between the 'TrapezoidalFuzzyNumbers' contained in two 'TrapezoidalFuzzyNumberLists'. See Sinova et al. (2013) [6] and Sinova et al. (2016) [10].

Usage

TrapezoidalFuzzyNumberList$dwablphi(s = NA, a = 1, b = 1, theta = 1)

Arguments

Details

See examples.

Returns

a matrix containing the ($\phi$,$\theta$)-wabl/ldev/rdev distances between the two previous mentioned TrapezoidalFuzzyNumberLists.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dwablphi(
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dwablphi(
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))),5,1,1)

# Example 3:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(20L)
F$dwablphi(S)

Method gsi()

This method calculates the Gini-Simpson diversity index for a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList'. See De la Rosa de Saa et al. (2015) [1].

Usage

TrapezoidalFuzzyNumberList$gsi()

Details

See examples.

Returns

the Gini-Simpson diversity index, which is a real number.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$gsi()

# Example 2:
F=Simulation$new()$simulCase1(50L)
F$gsi()

Method hyperI()

This method calculates the hyperbolic inequality index for a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList'. The method checks if all 'TrapezoidalFuzzyNumbers' are positive. See De la Rosa de Saa et al. (2015) [1] and Lubiano and Gil (2002) [4].

Usage

TrapezoidalFuzzyNumberList$hyperI(c = 0, verbose = TRUE)

Arguments

Details

See examples.

Returns

the hyperbolic inequality index, which is a real number. If the body's method inner conditions are not met, NA will be returned.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$hyperI()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$hyperI(0.5)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,4,6,8)))$hyperI()

# Example 4:
F=Simulation$new()$simulFRSTra(100L,0.05,0.35,0.6,2,1)
F$hyperI()

# Example 5:
F=Simulation$new()$simulCase2(10L)
F$hyperI(0.5)

Method mEstimator()

This method calculates the M-estimator of scale with loss method given in a 'TrapezoidalFuzzyNumberList' containing 'TrapezoidalFuzzyNumbers'. For computing the M-estimator, a method called “iterative reweighting” is used. The employed metric in the M-equation can be the 1-norm distance, the mid/spr distance or the ($\phi$,$\theta$)-wabl/ldev/rdev distance.

Usage

TrapezoidalFuzzyNumberList$mEstimator(
  f = NA,
  estInitial = NA,
  delta = NA,
  epsilon = NA,
  type = NA,
  a = 1,
  b = 1,
  theta = 1
)

Arguments

Details

See examples.

Returns

the value of the M-estimator of scale, which is a real number.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Huber",0.321,0.5,10^(-5),
1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Tukey",0.123,0.5,10^(-5),
2L,1,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Cauchy",0.123,0.5,10^(-5),
3L,0.75,0.5,1)

# Example 4:
F=Simulation$new()$simulCase1(100L)
U=F$median1Norm()
estInitial=F$mdd(U,1L)
delta=0.5
epsilon=10^(-5)
F$mEstimator("Huber",estInitial,delta,epsilon,1L)

Method mdd()

This method calculates the scale measure Median Distance Deviation (MDD) of a 'TrapezoidalFuzzyNumberList' with respect to a 'TrapezoidalFuzzyNumberList' or with respect to a 'FuzzyNumberList' with a unique valid fuzzy number. The employed metric in the calculation can be the 1-norm distance, the mid/spr distance or the ($\phi$,$\theta$)-wabl/ldev/rdev distance. See De la Rosa de Saa et al. (2015) [2] and De la Rosa de Saa et al. (2021) [3].

Usage

TrapezoidalFuzzyNumberList$mdd(s = NA, type = NA, a = 1, b = 1, theta = 1)

Arguments

Details

See examples.

Returns

the scale measure MDD, which is a real number.If the body's method inner conditions are not met, NA will be returned.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
3.0, 2.0, 1.0), dim = c(3, 3))))),1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
3.0, 2.0, 1.0), dim = c(3, 3))))),2L,2,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(5,6,7,8))),3L,1,1,1)

# Example 4:
F=Simulation$new()$simulCase3(10L)
U=F$mean()
F$mdd(U,3L,1,2,1)

# Example 5:
F=Simulation$new()$simulCase2(10L)
U=F$median1Norm()
F$mdd(U,2L)

# Example 6:
F=Simulation$new()$simulCase2(10L)
U=Simulation$new()$simulCase2(1L)
F$mdd(U,2L)

# Example 7:
F=Simulation$new()$simulCase2(10L)
U=F$transfTra()
F$mdd(U,2L)

# Example 8:
F=Simulation$new()$simulCase2(10L)
U=Simulation$new()$simulCase2(2L)
F$mdd(U,2L)

Method mean()

Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList', the method calculates the Aumann-type mean of these numbers (which is a 'TrapezoidalFuzzyNumber' too). See Sinova et al. (2015) [7].

Usage

TrapezoidalFuzzyNumberList$mean()

Details

See examples.

Returns

the Aumann-type mean, given as a TrapezoidalFuzzyNumber contained in a TrapezoidalFuzzyNumberList.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mean()

# Example 2:
TrapezoidalFuzzyNumberList$new(
c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$mean()

# Example 3:
F=Simulation$new()$simulCase1(100L)
F$mean()

Method median1Norm()

Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList', the method calculates the 1-norm median of these numbers, characterized by means of nl equidistant $\alpha$-levels (by default nl=101), including always the 0 and 1 levels, with their infimum and supremum values. See Sinova et al. (2012) [8].

Usage

TrapezoidalFuzzyNumberList$median1Norm(nl = 101L)

Arguments

Details

See examples.

Returns

the 1-norm median, given in form of a FuzzyNumber contained in a FuzzyNumberList.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$median1Norm()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$median1Norm(200L)

# Example 3:
F=Simulation$new()$simulCase1(10L)
F$median1Norm(200L)

Method medianWabl()

Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList', the method calculates the $\phi$-wabl/ldev/rdev median of these numbers, characterized by means of nl equidistant $\alpha$-levels (by default nl=101), including always the 0 and 1 levels, with their infimum and supremum values. See Sinova et al. (2013) [6] and Sinova et al. (2016) [10].

Usage

TrapezoidalFuzzyNumberList$medianWabl(nl = 101L, a = 1, b = 1)

Arguments

Details

See examples.

Returns

the $\phi$-wabl/ldev/rdev median in form of a FuzzyNUmber given in a FuzzyNumberList.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl(3L)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl(3L,2.2,2.8)

# Example 4:
F=Simulation$new()$simulCase1(10L)
F$medianWabl(3L)

Method qn()

This method calculates scale measure Qn for a matrix of 'TrapezoidalFuzzyNumbers' contained in the current 'TrapezoidalFuzzyNumber'. The employed metric in the calculation can be the 1-norm distance, the mid/spr distance or the ($\phi$,$\theta$)-wabl/ldev/rdev distance. See De la Rosa de Saa et al. (2021) [3].

Usage

TrapezoidalFuzzyNumberList$qn(type = NA, a = 1, b = 1, theta = 1)

Arguments

Details

See examples.

Returns

the scale measure Qn, which is a real number.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(2L,5,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(3L,1,1,1)

# Example 4:
F=Simulation$new()$simulCase1(10L)
F$qn(3L,1,1,1)

Method rho1()

This method calculates the 1-norm distance between the 'TrapezoidalFuzzyNumbers' contained in two 'TrapezoidalFuzzyNumberLists'.

Usage

TrapezoidalFuzzyNumberList$rho1(s = NA)

Arguments

Details

See examples.

Returns

a matrix containing the 1-norm distances between the two previous mentioned TrapezoidalFuzzyNumberLists.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$rho1(TrapezoidalFuzzyNumberList$new(
c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))

# Example 2:
F=Simulation$new()$simulCase1(4L)
S=Simulation$new()$simulCase1(5L)
F$rho1(S)
S$rho1(F)

Method sn()

This method calculates scale measure Sn for a matrix of 'TrapezoidalFuzzyNumbers' contained in the current 'TrapezoidalFuzzyNumber'. The employed metric in the calculation can be the 1-norm distance, the mid/spr distance or the ($\phi$,$\theta$)-wabl/ldev/rdev distance. See De la Rosa de Saa et al. (2021) [3].

Usage

TrapezoidalFuzzyNumberList$sn(type = NA, a = 1, b = 1, theta = 1)

Arguments

Details

See examples.

Returns

the scale measure Sn, which is a real number.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(2L,1,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(3L,5,1,0.5)

# Example 4:
F=Simulation$new()$simulCase1(10L)
F$sn(2L,5,1,0.5)

Method tn()

This method calculates scale measure Tn for a matrix of 'TrapezoidalFuzzyNumbers' contained in the current 'TrapezoidalFuzzyNumber'. The employed metric in the calculation can be the 1-norm distance, the mid/spr distance or the ($\phi$,$\theta$)-wabl/ldev/rdev distance. See De la Rosa de Saa et al. (2021) [3].

Usage

TrapezoidalFuzzyNumberList$tn(type = NA, a = 1, b = 1, theta = 1)

Arguments

Details

See examples.

Returns

the scale measure Tn, which is a real number.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(2L,1,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(3L,5,1,0.5)

# Example 4:
F=Simulation$new()$simulCase1(10L)
F$tn(1L)

Method transfTra()

This method transforms a 'TrapezoidalFuzzyNumberList' containing valid 'TrapezoidalFuzzyNumbers' characterized by their four values inf0, inf1, sup1, sup0 into a 'FuzzyNumberList' containing these same amount of fuzzy numbers, characterized by means of nl equidistant $\alpha$-levels each (by default nl=101).

Usage

TrapezoidalFuzzyNumberList$transfTra(nl = 101L)

Arguments

Details

See examples.

Returns

a FuzzyNumberList containing the transformed TrapezoidalFuzzyNumbers into FuzzyNumbers.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra(3L)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra(10L)

# Example 4:
F=Simulation$new()$simulCase3(10L)
F$transfTra(200L)

Method var()

Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList', the method calculates the variance of these numbers with respect to the mid/spr distance. See De la Rosa de Saa et al. (2017) [2].

Usage

TrapezoidalFuzzyNumberList$var(a = 1, b = 1, theta = 1)

Arguments

Details

See examples.

Returns

the variance of the sample with respect to the mid/spr distance, which is a real number.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var(1,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var(1/3,1/3,1/5)

# Example 4:
F=Simulation$new()$simulCase1(10L)
F$var(1,1,1)

Method wablphi()

Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList', the method calculates the $\phi$-wabl value for each of these numbers. See Sinova et al. (2014) [9].

Usage

TrapezoidalFuzzyNumberList$wablphi(a = 1, b = 1)

Arguments

Details

See examples.

Returns

a vector giving the $\phi$-wabl values of each TrapezoidalFuzzyNumber.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi(2,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi(2.2,1.1)

# Example 4:
F=Simulation$new()$simulCase4(60L)
F$wablphi(2,1)

Method addTrapezoidalFuzzyNumber()

This method adds a 'TrapezoidalFuzzyNumber' to the current collection inside the current 'TrapezoidalFuzzyNumberList'. Therefore, the dimensions' field is increased in a unit.

Usage

TrapezoidalFuzzyNumberList$addTrapezoidalFuzzyNumber(n = NA, verbose = TRUE)

Arguments

Details

See examples.

Returns

nothing.

Examples

TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4))
)$addTrapezoidalFuzzyNumber(TrapezoidalFuzzyNumber$new(3,4,5,6))

Method removeTrapezoidalFuzzyNumber()

This method removes a 'TrapezoidalFuzzyNumber' to the current collection inside the current 'TrapezoidalFuzzyNumberList'. Therefore, the dimensions' field is decreased in a unit.

Usage

TrapezoidalFuzzyNumberList$removeTrapezoidalFuzzyNumber(i = NA, verbose = TRUE)

Arguments

Details

See examples.

Returns

nothing.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,3,4,4)))$removeTrapezoidalFuzzyNumber(1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,3,4,4)))$removeTrapezoidalFuzzyNumber(2L)

Method getDimension()

This method gives the number contained in the dimension passed as parameter when the dimension is greater than 0 and not greater than the dimensions of the TrapezoidalFuzzyNumberList's numbers array.

Usage

TrapezoidalFuzzyNumberList$getDimension(i = NA)

Arguments

Details

See examples.

Returns

The TrapezoidalFuzzyNumber contained in the dimension passed as parameter or an error if the dimension is not valid.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,3,4,4)))$getDimension(1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,3,4,4)))$getDimension(2L)

Method plot()

This method shows in a graph the values of the attribute numbers of the corresponding 'TrapezoidalFuzzyNumberList'.

Usage

TrapezoidalFuzzyNumberList$plot(color = "grey")

Arguments

Details

See examples.

Returns

a graph with the values of the attribute numbers of the corresponding 'TrapezoidalFuzzyNumberList'.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,3,4,5)))$plot()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
TrapezoidalFuzzyNumber$new(-6,0,1,4)))$plot()

# Example 3:
Simulation$new()$simulCase1(8L)$plot(palette())

# Example 4:
Simulation$new()$simulCase1(5L)$plot(palette()[2:6])

Method getLength()

This method returns the number of dimensions that are equivalent to the number of 'TrapezoidalFuzzyNumbers' in the corresponding 'TrapezoidalFuzzyNumberList'.

Usage

TrapezoidalFuzzyNumberList$getLength()

Details

See examples.

Returns

the number of dimensions that are equivalent to the number of 'TrapezoidalFuzzyNumbers' in the corresponding 'TrapezoidalFuzzyNumberList'.

Examples

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4))
)$getLength()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
TrapezoidalFuzzyNumber$new(-6,0,1,4)))$getLength()

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
TrapezoidalFuzzyNumber$new(-6,0,1,4),TrapezoidalFuzzyNumber$new(1,2,3,4))
)$getLength()

Method clone()

The objects of this class are cloneable with this method.

Usage

TrapezoidalFuzzyNumberList$clone(deep = FALSE)

Arguments

Note

In case you find (almost surely existing) bugs or have recommendations for improving the method, comments are welcome to the above mentioned mail addresses.

Author(s)

(s) Andrea Garcia Cernuda <[email protected]>, Asun Lubiano <[email protected]>, Sara de la Rosa de Saa

References

[1] De la Rosa de Saa, S.; Gil, M.A.; Gonzalez-Rodriguez, G.; Lopez, M.T.; Lubiano M.A.: Fuzzy rating scale-based questionnaires and their statistical analysis, IEEE Transactions on Fuzzy Systems 23(1), 111-126 (2015)

[2] De la Rosa de Saa, S.; Lubiano M.A.; Sinova, B.; Filzmoser, P.: Robust scale estimators for fuzzy data, Advances in Data Analysis and Classification 11(4), 731-758 (2017)

[3] De la Rosa de Sáa, S.; Lubiano, M.A.; Sinova, B.; Filzmoser, P.; Gil, M.Á.: Location-free robust scale estimates for fuzzy data, IEEE Transactions on Fuzzy Systems 29(6), 1682-1694 (2021)

[4] Lubiano, M.A.; Gil, M.A.: f-Inequality indices for fuzzy random variables, in Statistical Modeling, Analysis and Management of Fuzzy Data (Bertoluzza, C., Gil, M.A., Ralescu, D.A., Eds.), Physica-Verlag, 43-63 (2002)

[5] Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications, European Journal of Operational Research 251, 918-929 (2016)

[6] Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: A generalized L1-type metric between fuzzy numbers for an approach to central tendency of fuzzy data, Information Sciences 242, 22-34 (2013)

[7] Sinova, B.; De la Rosa de Saa, S.; Lubiano, M.A.; Gil, M.A.: An overview on the statistical central tendency for fuzzy datasets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 23 (Suppl. 1), 105-132 (2015)

[8] 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 200, 99-115 (2012)

[9] Sinova, B.; Gil, M.A.; Lopez, M.T.; Van Aelst, S.: A parameterized L2 metric between fuzzy numbers and its parameter interpretation, Fuzzy Sets and Systems 245, 101-115 (2014)

[10] Sinova, B.; Gil, M.A.; Van Aelst, S.: M-estimates of location for the robust central tendency of fuzzy data, IEEE Transactions on Fuzzy Systems 24(4), 945-956 (2016)

Examples

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$new`
## ------------------------------------------------

TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1, 2, 3, 4),
TrapezoidalFuzzyNumber$new(-8, -6, -4, -2),
TrapezoidalFuzzyNumber$new(-1, -1, 2, 3),
TrapezoidalFuzzyNumber$new(1, 2, 3, 3)))

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$add`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
3.0, 2.0, 1.0), dim = c(3, 3))))),1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
3.0, 2.0, 1.0), dim = c(3, 3))))),2L,2,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(5,6,7,8))),3L,1,1,1)

# Example 4:
F=Simulation$new()$simulCase1(10L)
S=F$mean()
F$add(S,1L)

# Example 5:
F=Simulation$new()$simulCase1(100L)
S=F$median1Norm()
F$add(S,2L,2,1,1)

# Example 6:
F=Simulation$new()$simulCase2(10L)
U=Simulation$new()$simulCase2(1L)
F$add(U,2L)

# Example 7:
F=Simulation$new()$simulCase2(10L)
U=F$transfTra()
F$add(U,2L)

# Example 8:
F=Simulation$new()$simulCase2(10L)
U=Simulation$new()$simulCase2(2L)
F$add(U,2L)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$dthetaphi`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dthetaphi(
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dthetaphi(
TrapezoidalFuzzyNumberList$new( c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))),1,1,1)

# Example 3:
F=Simulation$new()$simulCase1(6L)
S=Simulation$new()$simulCase1(8L)
F$dthetaphi(S,1,5,1)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$dwablphi`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dwablphi(
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dwablphi(
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))),5,1,1)

# Example 3:
F=Simulation$new()$simulCase1(10L)
S=Simulation$new()$simulCase1(20L)
F$dwablphi(S)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$gsi`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$gsi()

# Example 2:
F=Simulation$new()$simulCase1(50L)
F$gsi()

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$hyperI`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$hyperI()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$hyperI(0.5)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,4,6,8)))$hyperI()

# Example 4:
F=Simulation$new()$simulFRSTra(100L,0.05,0.35,0.6,2,1)
F$hyperI()

# Example 5:
F=Simulation$new()$simulCase2(10L)
F$hyperI(0.5)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$mEstimator`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Huber",0.321,0.5,10^(-5),
1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Tukey",0.123,0.5,10^(-5),
2L,1,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Cauchy",0.123,0.5,10^(-5),
3L,0.75,0.5,1)

# Example 4:
F=Simulation$new()$simulCase1(100L)
U=F$median1Norm()
estInitial=F$mdd(U,1L)
delta=0.5
epsilon=10^(-5)
F$mEstimator("Huber",estInitial,delta,epsilon,1L)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$mdd`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
3.0, 2.0, 1.0), dim = c(3, 3))))),1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
3.0, 2.0, 1.0), dim = c(3, 3))))),2L,2,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(5,6,7,8))),3L,1,1,1)

# Example 4:
F=Simulation$new()$simulCase3(10L)
U=F$mean()
F$mdd(U,3L,1,2,1)

# Example 5:
F=Simulation$new()$simulCase2(10L)
U=F$median1Norm()
F$mdd(U,2L)

# Example 6:
F=Simulation$new()$simulCase2(10L)
U=Simulation$new()$simulCase2(1L)
F$mdd(U,2L)

# Example 7:
F=Simulation$new()$simulCase2(10L)
U=F$transfTra()
F$mdd(U,2L)

# Example 8:
F=Simulation$new()$simulCase2(10L)
U=Simulation$new()$simulCase2(2L)
F$mdd(U,2L)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$mean`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mean()

# Example 2:
TrapezoidalFuzzyNumberList$new(
c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$mean()

# Example 3:
F=Simulation$new()$simulCase1(100L)
F$mean()

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$median1Norm`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$median1Norm()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$median1Norm(200L)

# Example 3:
F=Simulation$new()$simulCase1(10L)
F$median1Norm(200L)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$medianWabl`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl(3L)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl(3L,2.2,2.8)

# Example 4:
F=Simulation$new()$simulCase1(10L)
F$medianWabl(3L)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$qn`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(2L,5,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(3L,1,1,1)

# Example 4:
F=Simulation$new()$simulCase1(10L)
F$qn(3L,1,1,1)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$rho1`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$rho1(TrapezoidalFuzzyNumberList$new(
c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))

# Example 2:
F=Simulation$new()$simulCase1(4L)
S=Simulation$new()$simulCase1(5L)
F$rho1(S)
S$rho1(F)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$sn`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(2L,1,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(3L,5,1,0.5)

# Example 4:
F=Simulation$new()$simulCase1(10L)
F$sn(2L,5,1,0.5)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$tn`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(2L,1,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(3L,5,1,0.5)

# Example 4:
F=Simulation$new()$simulCase1(10L)
F$tn(1L)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$transfTra`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra(3L)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra(10L)

# Example 4:
F=Simulation$new()$simulCase3(10L)
F$transfTra(200L)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$var`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var(1,1,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var(1/3,1/3,1/5)

# Example 4:
F=Simulation$new()$simulCase1(10L)
F$var(1,1,1)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$wablphi`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi(2,1)

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi(2.2,1.1)

# Example 4:
F=Simulation$new()$simulCase4(60L)
F$wablphi(2,1)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$addTrapezoidalFuzzyNumber`
## ------------------------------------------------

TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4))
)$addTrapezoidalFuzzyNumber(TrapezoidalFuzzyNumber$new(3,4,5,6))

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$removeTrapezoidalFuzzyNumber`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,3,4,4)))$removeTrapezoidalFuzzyNumber(1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,3,4,4)))$removeTrapezoidalFuzzyNumber(2L)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$getDimension`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,3,4,4)))$getDimension(1L)

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,3,4,4)))$getDimension(2L)

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$plot`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
TrapezoidalFuzzyNumber$new(2,3,4,5)))$plot()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
TrapezoidalFuzzyNumber$new(-6,0,1,4)))$plot()

# Example 3:
Simulation$new()$simulCase1(8L)$plot(palette())

# Example 4:
Simulation$new()$simulCase1(5L)$plot(palette()[2:6])

## ------------------------------------------------
## Method `TrapezoidalFuzzyNumberList$getLength`
## ------------------------------------------------

# Example 1:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4))
)$getLength()

# Example 2:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
TrapezoidalFuzzyNumber$new(-6,0,1,4)))$getLength()

# Example 3:
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
TrapezoidalFuzzyNumber$new(-6,0,1,4),TrapezoidalFuzzyNumber$new(1,2,3,4))
)$getLength()