ADD: Average Distance Deviation of a trapezoidal fuzzy sample with...
In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

Description Usage Arguments Details Value Note Author(s) References See Also Examples

This function calculates the scale measure Average Distance Deviation (ADD) for a matrix of trapezoidal fuzzy numbers F with respect to a fuzzy number U. The employed metric in the calculation can be the 1-norm distance, the mid/spr distance or the (\varphi,θ)-wabl/ldev/rdev distance. The function first checks if the input matrix F is given in the correct form (tested by checkingTra) and also the input fuzzy number U (tested by checking or checkingTra).

1	ADD(F, U, type, a = 1, b = 1, theta = 1/3)

`F`	matrix of dimension `n x 4` containing `n` trapezoidal fuzzy numbers characterized by their four values `inf0,inf1,sup1,sup0`. The function implicitly checks if the matrix is in the correct form (tested by `checkingTra`).
`U`	can be a matrix of dimension `1 x 4` (trapezoidal fuzzy number) or an array of dimension `nl x 3 x 1` (general fuzzy number), where `nl` is the number of considered α-levels and 3 the number of columns of the array: the first column will be the α-levels, the second one their infimum values and the third one their supremum values. The function implicitly checks if the fuzzy number `U` is in the correct form (tested by `checking` if `U` is an array and tested by `checkingTra` if `U` is a matrix).
`type`	number 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 (\varphi,θ)-wabl/ldev/rdev distance will be used.
`a`	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 (\varphi,θ)-wabl/ldev/rdev distance.
`b`	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 (\varphi,θ)-wabl/ldev/rdev distance.
`theta`	number >0, by default `theta`=1/3. It is the weight of the spread in the mid/spr distance and the weight of the ldev and rdev in the (\varphi,θ)-wabl/ldev/rdev distance.

See examples

The function returns the scale measure ADD, which is a real number.

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

Asun Lubiano <lubiano@uniovi.es>, Sara de la Rosa de Saa <rosasara@uniovi.es>

[1] 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, pp. 1-28 (2015)

checkingTra, checking, TransfTra, Rho1Tra, Rho1, DthetaphiTra, Dthetaphi, DwablphiTra, Dwablphi

# Example 1:
F=SimulCASE1(10)
U=Mean(F)
ADD(F,U,1)

# Example 2:
F=SimulCASE1(100)
U=Median1norm(F)
ADD(F,U,2,2,1,1)

# Example 3:
F=SimulCASE1(100)
U=matrix(c(1,2,3,2),nrow=1)
ADD(F,U,1)

# Example 4:
F=matrix(1:4,nrow=2)
U=matrix(1:4,nrow=1)
ADD(F,U,3,1,1,1)