TrapezoidalFuzzyNumberList {FuzzyStatTraEOO} | R Documentation |
'TrapezoidalFuzzyNumberList' must contain valid 'TrapezoidalFuzzyNumbers'. This class implements a version of the empty 'StatList' methods.
FuzzyStatTraEOO::StatList
-> TrapezoidalFuzzyNumberList
new()
This method creates a 'TrapezoidalFuzzyNumberList' object with all the attributes set if the 'TrapezoidalFuzzyNumbers' are valid.
TrapezoidalFuzzyNumberList$new(numbers = NA)
numbers
is a list which contains n TrapezoidalFuzzyNumbers.
See examples.
The TrapezoidalFuzzyNumberList object created with all attributes set if the 'TrapezoidalFuzzyNumbers' are valid.
TrapezoidalFuzzyNumberList$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)))
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].
TrapezoidalFuzzyNumberList$add(s = NA, type = NA, a = 1, b = 1, theta = 1)
s
is a TrapezoidalFuzzyNumberList containing a unique valid TrapezoidalFuzzyNumber or it is a FuzzyNumberList containing a unique valid FuzzyNumber.
type
positive integer 1, 2 or 3: if type==1, the 1-norm distance will
be considered in the calculation of the measure ADD. If type==2, the mid/spr
distance will be considered. By contrast, if type==3, the (\phi
,\theta
)-wabl/ldev/rdev
distance will be used.
a
real number > 0, by default a=1. It is the first parameter of a
beta distribution which corresponds to a weighting measure on [0,1] in the
mid/spr distance or in the (\phi
,\theta
)-wabl/ldev/rdev distance.
b
real number > 0, by default b=1. It is the second parameter of a
beta distribution which corresponds to a weighting measure on [0,1] in the
mid/spr distance or in the (\phi
,\theta
)-wabl/ldev/rdev distance.
theta
real number > 0, by default theta=1. It is the weight of the
spread in the mid/spr distance and the weight of the ldev and rdev in the
(\phi
,\theta
)-wabl/ldev/rdev distance.
See examples.
the scale measure ADD, which is a real number. If the body's method inner conditions are not met, NA will be returned.
# Example 1: TrapezoidalFuzzyNumberList$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)
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].
TrapezoidalFuzzyNumberList$dthetaphi(s = NA, a = 1, b = 1, theta = 1)
s
TrapezoidalFuzzyNumberList containing valid TrapezoidalFuzzyNumbers characterized by their four values inf0, inf1, sup1, sup0.
a
real number > 0, by default a=1. It is the first parameter of a beta distribution which corresponds to a weighting measure on [0,1].
b
real number > 0, by default b=1. It is the second parameter of a beta distribution which corresponds to a weighting measure on [0,1].
theta
real number > 0, by default theta=1. It is the weight of the spread in the mid/spr distance.
See examples.
a matrix containing the mid/spr distances between the two previous mentioned TrapezoidalFuzzyNumberLists.
# Example 1: TrapezoidalFuzzyNumberList$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)
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].
TrapezoidalFuzzyNumberList$dwablphi(s = NA, a = 1, b = 1, theta = 1)
s
TrapezoidalFuzzyNumberList containing valid TrapezoidalFuzzyNumbers characterized by their four values inf0, inf1, sup1, sup0.
a
real number > 0, by default a=1. It is the first parameter of a beta distribution which corresponds to a weighting measure on [0,1].
b
real number > 0, by default b=1. It is the second parameter of a beta distribution which corresponds to a weighting measure on [0,1].
theta
real number > 0, by default theta=1. It is the weight of the
ldev and rdev in the (\phi
,\theta
)-wabl/ldev/rdev distance.
See examples.
a matrix containing the (\phi
,\theta
)-wabl/ldev/rdev distances
between the two previous mentioned TrapezoidalFuzzyNumberLists.
# Example 1: TrapezoidalFuzzyNumberList$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)
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].
TrapezoidalFuzzyNumberList$gsi()
See examples.
the Gini-Simpson diversity index, which is a real number.
# Example 1: TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4), TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$gsi() # Example 2: F=Simulation$new()$simulCase1(50L) F$gsi()
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].
TrapezoidalFuzzyNumberList$hyperI(c = 0, verbose = TRUE)
c
number in [0,0.5]. The c*100 of the hyperbolic inequality index.
verbose
if TRUE the messages are written to the console unless the user actively decides to set verbose=FALSE.
See examples.
the hyperbolic inequality index, which is a real number. If the body's method inner conditions are not met, NA will be returned.
# Example 1: TrapezoidalFuzzyNumberList$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$hyperI(0.5)
mEstimator()
This method calculates the M-estimator of scale with loss method given
in a 'TrapezoidalFuzzyNumberList' containing 'TrapezoidalFuzzyNumbers'.
For computing the M-estimator, a method called “iterative reweighting” is
used. The employed metric in the M-equation can be the 1-norm distance, the
mid/spr distance or the (\phi
,\theta
)-wabl/ldev/rdev distance.
TrapezoidalFuzzyNumberList$mEstimator( f = NA, estInitial = NA, delta = NA, epsilon = NA, type = NA, a = 1, b = 1, theta = 1 )
f
is the name of the loss function. It can be "Huber", "Tukey" or "Cauchy".
estInitial
real number > 0.
delta
real number in (0,1). It is present in the f-equation.
epsilon
real number > 0. It is the tolerance allowed in the algorithm.
type
positive integer 1, 2 or 3: if type==1, the 1-norm distance will
be considered in the calculation of the measure ADD. If type==2, the mid/spr
distance will be considered. By contrast, if type==3, the (\phi
,\theta
)-wabl/ldev/rdev
distance will be used.
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] in the
mid/spr distance or in the (\phi
,\theta
)-wabl/ldev/rdev distance.
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] in the
mid/spr distance or in the (\phi
,\theta
)-wabl/ldev/rdev distance.
theta
real number > 0, by default theta=1. It is the weight of the
spread in the mid/spr distance and the weight of the ldev and rdev in the
(\phi
,\theta
)-wabl/ldev/rdev distance.
See examples.
the value of the M-estimator of scale, which is a real number.
# 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$mEstimator("Huber",estInitial,delta,epsilon,1L)
mdd()
This method calculates the scale measure Median Distance Deviation (MDD)
of a 'TrapezoidalFuzzyNumberList' with respect to a 'TrapezoidalFuzzyNumberList'
or with respect to a 'FuzzyNumberList' with a unique valid fuzzy number.
The employed metric in the calculation can be the 1-norm distance, the mid/spr
distance or the (\phi
,\theta
)-wabl/ldev/rdev distance.
See De la Rosa de Saa et al. (2015) [2] and De la Rosa de Saa et al. (2021) [3].
TrapezoidalFuzzyNumberList$mdd(s = NA, type = NA, a = 1, b = 1, theta = 1)
s
is a TrapezoidalFuzzyNumberList containing a unique TrapezoidalFuzzyNumber or it is a FuzzyNumberList containing a unique FuzzyNumber.
type
positive integer 1, 2 or 3: if type==1, the 1-norm distance will
be considered in the calculation of the measure ADD. If type==2, the mid/spr
distance will be considered. By contrast, if type==3, the (\phi
,\theta
)-wabl/ldev/rdev
distance will be used.
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] in the
mid/spr distance or in the (\phi
,\theta
)-wabl/ldev/rdev distance.
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] in the
mid/spr distance or in the (\phi
,\theta
)-wabl/ldev/rdev distance.
theta
real number > 0, by default theta=1. It is the weight of the
spread in the mid/spr distance and the weight of the ldev and rdev in the
(\phi
,\theta
)-wabl/ldev/rdev distance.
See examples.
the scale measure MDD, which is a real number.If the body's method inner conditions are not met, NA will be returned.
# 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$mdd(U,2L)
mean()
Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList', the method calculates the Aumann-type mean of these numbers (which is a 'TrapezoidalFuzzyNumber' too). See Sinova et al. (2015) [7].
TrapezoidalFuzzyNumberList$mean()
See examples.
the Aumann-type mean, given as a TrapezoidalFuzzyNumber contained in a TrapezoidalFuzzyNumberList.
# 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$mean()
median1Norm()
Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
the method calculates the 1-norm median of these numbers, characterized
by means of nl equidistant \alpha
-levels (by default nl=101), including
always the 0 and 1 levels, with their infimum and supremum values.
See Sinova et al. (2012) [8].
TrapezoidalFuzzyNumberList$median1Norm(nl = 101L)
nl
integer greater or equal to 2, by default nl=101. It indicates the
number of desired \alpha
-levels for characterizing the 1-norm median.
See examples.
the 1-norm median, given in form of a FuzzyNumber contained in a FuzzyNumberList.
# 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$median1Norm(200L)
medianWabl()
Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
the method calculates the \phi
-wabl/ldev/rdev median of these numbers,
characterized by means of nl equidistant \alpha
-levels (by default nl=101),
including always the 0 and 1 levels, with their infimum and supremum values.
See Sinova et al. (2013) [6] and Sinova et al. (2016) [10].
TrapezoidalFuzzyNumberList$medianWabl(nl = 101L, a = 1, b = 1)
nl
integer greater or equal to 2, by default nl=101. It indicates the
number of desired \alpha
-levels for characterizing the \phi
-wabl/ldev/rdev
median.
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].
See examples.
the \phi
-wabl/ldev/rdev median in form of a FuzzyNUmber given
in a FuzzyNumberList.
# 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$medianWabl(3L)
qn()
This method calculates scale measure Qn for a matrix of 'TrapezoidalFuzzyNumbers'
contained in the current 'TrapezoidalFuzzyNumber'. The employed metric
in the calculation can be the 1-norm distance, the mid/spr distance or the
(\phi
,\theta
)-wabl/ldev/rdev distance.
See De la Rosa de Saa et al. (2021) [3].
TrapezoidalFuzzyNumberList$qn(type = NA, a = 1, b = 1, theta = 1)
type
integer number that can be 1, 2 or 3: if type==1, the 1-norm
distance will be considered in the calculation of the measure ADD. If type==2,
the mid/spr distance will be considered. By contrast, if type==3, the
(\phi
,\theta
)-wabl/ldev/rdev distance will be used.
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] in the
mid/spr distance or the (\phi
,\theta
)-wabl/ldev/rdev distance.
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] in the
mid/spr distance or the (\phi
,\theta
)-wabl/ldev/rdev distance.
theta
real number > 0, by default theta=1. It is the weight of the
spread in the mid/spr distance and the weight of the ldev and rdev in the
(\phi
,\theta
)-wabl/ldev/rdev distance.
See examples.
the scale measure Qn, which is a real number.
# 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$qn(3L,1,1,1)
rho1()
This method calculates the 1-norm distance between the 'TrapezoidalFuzzyNumbers' contained in two 'TrapezoidalFuzzyNumberLists'.
TrapezoidalFuzzyNumberList$rho1(s = NA)
s
TrapezoidalFuzzyNumberList containing valid TrapezoidalFuzzyNumbers characterized by their four values inf0, inf1, sup1, sup0.
See examples.
a matrix containing the 1-norm distances between the two previous mentioned TrapezoidalFuzzyNumberLists.
# 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$rho1(F)
sn()
This method calculates scale measure Sn for a matrix of 'TrapezoidalFuzzyNumbers'
contained in the current 'TrapezoidalFuzzyNumber'. The employed metric
in the calculation can be the 1-norm distance, the mid/spr distance or the
(\phi
,\theta
)-wabl/ldev/rdev distance.
See De la Rosa de Saa et al. (2021) [3].
TrapezoidalFuzzyNumberList$sn(type = NA, a = 1, b = 1, theta = 1)
type
integer number that can be 1, 2 or 3: if type==1, the 1-norm
distance will be considered in the calculation of the measure ADD. If type==2,
the mid/spr distance will be considered. By contrast, if type==3, the
(\phi
,\theta
)-wabl/ldev/rdev distance will be used.
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] in the
mid/spr distance or the (\phi
,\theta
)-wabl/ldev/rdev distance.
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] in the
mid/spr distance or the (\phi
,\theta
)-wabl/ldev/rdev distance.
theta
real number > 0, by default theta=1. It is the weight of the
spread in the mid/spr distance and the weight of the ldev and rdev in the
(\phi
,\theta
)-wabl/ldev/rdev distance.
See examples.
the scale measure Sn, which is a real number.
# 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$sn(2L,5,1,0.5)
tn()
This method calculates scale measure Tn for a matrix of 'TrapezoidalFuzzyNumbers'
contained in the current 'TrapezoidalFuzzyNumber'. The employed metric
in the calculation can be the 1-norm distance, the mid/spr distance or the
(\phi
,\theta
)-wabl/ldev/rdev distance.
See De la Rosa de Saa et al. (2021) [3].
TrapezoidalFuzzyNumberList$tn(type = NA, a = 1, b = 1, theta = 1)
type
integer number that can be 1, 2 or 3: if type==1, the 1-norm
distance will be considered in the calculation of the measure ADD. If type==2,
the mid/spr distance will be considered. By contrast, if type==3, the
(\phi
,\theta
)-wabl/ldev/rdev distance will be used.
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] in the
mid/spr distance or the (\phi
,\theta
)-wabl/ldev/rdev distance.
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] in the
mid/spr distance or the (\phi
,\theta
)-wabl/ldev/rdev distance.
theta
real number > 0, by default theta=1. It is the weight of the
spread in the mid/spr distance and the weight of the ldev and rdev in the
(\phi
,\theta
)-wabl/ldev/rdev distance.
See examples.
the scale measure Tn, which is a real number.
# 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$tn(1L)
transfTra()
This method transforms a 'TrapezoidalFuzzyNumberList' containing valid
'TrapezoidalFuzzyNumbers' characterized by their four values inf0, inf1,
sup1, sup0 into a 'FuzzyNumberList' containing these same amount of fuzzy
numbers, characterized by means of nl equidistant \alpha
-levels each
(by default nl=101).
TrapezoidalFuzzyNumberList$transfTra(nl = 101L)
nl
integer greater or equal to 2, by default nl=101. It indicates the
number of desired \alpha
-levels for characterizing the trapezoidal
fuzzy numbers.
See examples.
a FuzzyNumberList containing the transformed TrapezoidalFuzzyNumbers into FuzzyNumbers.
# 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$transfTra(200L)
var()
Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList', the method calculates the variance of these numbers with respect to the mid/spr distance. See De la Rosa de Saa et al. (2017) [2].
TrapezoidalFuzzyNumberList$var(a = 1, b = 1, theta = 1)
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.
See examples.
the variance of the sample with respect to the mid/spr distance, which is a real number.
# 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$var(1,1,1)
wablphi()
Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
the method calculates the \phi
-wabl value for each of these numbers.
See Sinova et al. (2014) [9].
TrapezoidalFuzzyNumberList$wablphi(a = 1, b = 1)
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].
See examples.
a vector giving the \phi
-wabl values of each TrapezoidalFuzzyNumber.
# 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$wablphi(2,1)
addTrapezoidalFuzzyNumber()
This method adds a 'TrapezoidalFuzzyNumber' to the current collection inside the current 'TrapezoidalFuzzyNumberList'. Therefore, the dimensions' field is increased in a unit.
TrapezoidalFuzzyNumberList$addTrapezoidalFuzzyNumber(n = NA, verbose = TRUE)
n
is the TrapezoidalFuzzyNumber to be added to the current collection inside the current TrapezoidalFuzzyNumberList.
verbose
if TRUE the messages are written to the console unless the user actively decides to set verbose=FALSE.
See examples.
nothing.
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4)) )$addTrapezoidalFuzzyNumber(TrapezoidalFuzzyNumber$new(3,4,5,6))
removeTrapezoidalFuzzyNumber()
This method removes a 'TrapezoidalFuzzyNumber' to the current collection inside the current 'TrapezoidalFuzzyNumberList'. Therefore, the dimensions' field is decreased in a unit.
TrapezoidalFuzzyNumberList$removeTrapezoidalFuzzyNumber(i = NA, verbose = TRUE)
i
is the position of the TrapezoidalFuzzyNumber to be removed in the current collection inside the current TrapezoidalFuzzyNumberList.
verbose
if TRUE the messages are written to the console unless the user actively decides to set verbose=FALSE.
See examples.
nothing.
# Example 1: TrapezoidalFuzzyNumberList$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)))$removeTrapezoidalFuzzyNumber(2L)
getDimension()
This method gives the number contained in the dimension passed as parameter when the dimension is greater than 0 and not greater than the dimensions of the TrapezoidalFuzzyNumberList's numbers array.
TrapezoidalFuzzyNumberList$getDimension(i = NA)
i
is the dimension of the TrapezoidalFuzzyNumber wanted to be retrieved.
See examples.
The TrapezoidalFuzzyNumber contained in the dimension passed as parameter or an error if the dimension is not valid.
# 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)
plot()
This method shows in a graph the values of the attribute numbers of the corresponding 'TrapezoidalFuzzyNumberList'.
TrapezoidalFuzzyNumberList$plot(color = "grey")
color
is the color of the lines representing the numbers to be shown in the graph. The default value is grey, other colors can be specified, the option palette() too.
See examples.
a graph with the values of the attribute numbers of the corresponding 'TrapezoidalFuzzyNumberList'.
# Example 1: TrapezoidalFuzzyNumberList$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)$plot(palette()[2:6])
getLength()
This method returns the number of dimensions that are equivalent to the number of 'TrapezoidalFuzzyNumbers' in the corresponding 'TrapezoidalFuzzyNumberList'.
TrapezoidalFuzzyNumberList$getLength()
See examples.
the number of dimensions that are equivalent to the number of 'TrapezoidalFuzzyNumbers' in the corresponding 'TrapezoidalFuzzyNumberList'.
# 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()
clone()
The objects of this class are cloneable with this method.
TrapezoidalFuzzyNumberList$clone(deep = FALSE)
deep
Whether to make a deep clone.
In case you find (almost surely existing) bugs or have recommendations for improving the method, comments are welcome to the above mentioned mail addresses.
(s) Andrea Garcia Cernuda <uo270115@uniovi.es>, Asun Lubiano <lubiano@uniovi.es>, Sara de la Rosa de Saa
[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)
## ------------------------------------------------
## 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()