FuzzyNumberList {FuzzyStatTraEOO}

'FuzzyNumberList' is a child class of 'StatList'.

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()

Inherited methods

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

numbers

is a list of dimension nl x 3 x n which contains n fuzzy numbers. nl is the number of considered \alpha-levels and 3 is the number of columns of the list. The first column represents the number of considered \alpha-levels, the second one represents their infimum values and the third and last column represents their supremum values.

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

s

FuzzyNumberList containing FuzzyNumbers characterized by means of nl \alpha-levels each. The \alpha-levels of the FuzzyNumberList s should coincide with the ones of the current FuzzyNumberList (the method checks this condition).

a

real number > 0, by default a=1. It is the first parameter of a beta distribution which corresponds to a weighting measure on [0,1].

b

real number > 0, by default b=1. It is the second parameter of a beta distribution which corresponds to a weighting measure on [0,1].

theta

real number > 0, by default theta=1. It is the weight of the spread in the mid/spr distance.

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

s

FuzzyNumberList containing FuzzyNumbers characterized by means of nl \alpha-levels each. The \alpha-levels should coincide with ones of the other FuzzyNumberList (the method checks this condition).

a

real number > 0, by default a=1. It is the first parameter of a beta distribution which corresponds to a weighting measure on [0,1].

b

real number > 0, by default b=1. It is the second parameter of a beta distribution which corresponds to a weighting measure on [0,1].

theta

real number > 0, by default theta=1. It is the weight of the ldev and rdev in the (\phi,\theta)-wabl/ldev/rdev distance.

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

s

FuzzyNumberList containing FuzzyNumbers characterized by means of nl \alpha-levels each. The method checks that the \alpha-levels should coincide with ones of the other FuzzyNumberList.

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

n

is the FuzzyNumber to be added to the current collection of fuzzy numbers.

verbose

if TRUE the messages are written to the console unless the user actively decides to set verbose=FALSE.

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

i

is the position of the FuzzyNumber to be removed in the current collection of fuzzy numbers.

verbose

if TRUE the messages are written to the console unless the user actively decides to set verbose=FALSE.

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

i

is the dimension of the FuzzyNumber wanted to be retrieved.

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

color

is the color of the lines representing the numbers to be shown in the graph. The default value is grey, other colors can be specified, the option palette() too.

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

deep

Whether to make a deep clone.

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 <[e-mail]>, Asun Lubiano <[e-mail]>, 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()