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

## Description

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).

## Usage

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

## Arguments

 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

## Value

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

## Note

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

## Author(s)

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

## References

[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

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 # 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) 

FuzzyStatTra documentation built on May 2, 2019, 10:59 a.m.