# Medianwabl: \varphi-wabl/ldev/rdev median of a trapezoidal fuzzy sample In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

## Description

Given a sample of trapezoidal fuzzy numbers contained in a matrix F, the function calculates the \varphi-wabl/ldev/rdev median of these numbers, characterized by means of nl equidistant α-levels (by default nl=101), including always the 0 and 1 levels, with their infimum and supremum values. The function first checks if the input matrix F is given in the correct form (tested by checkingTra).

## Usage

 1 Medianwabl(F, nl = 101, a = 1, b = 1) 

## 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). nl positive integer, by default nl=101. It indicates the number of desired α-levels for characterizing the\varphi-wabl/ldev/rdev median. 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]. 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].

See examples

## Value

The function returns the \varphi-wabl/ldev/rdev median, given by an array of dimension nl x 3 x 1 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.

## 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

 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, pp. 22-34 (2013)

 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), pp. 945-956 (2016)

## See Also

checkingTra, DwablphiTra, Dwablphi, Wablphi, Median1norm

## Examples

 1 2 3 4 5 6 7 # Example 1: F=SimulCASE1(10) Medianwabl(F,3) # Example 2: F=matrix(c(1,0,2,3),nrow=1) Medianwabl(F) 

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