# Median1norm: 1-norm 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 1-norm 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 Median1norm(F, nl = 101) 

## 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 1-norm median.

See examples

## Value

The function returns the 1-norm 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

[1] Sinova, B.; Gil, M.A.; Colubi, A.; Van Aelst, S.: The median of a random fuzzy number. The 1-norm distance approach, Fuzzy Sets Syst. 200, pp. 99-115 (2012)

checkingTra, TransfTra, Medianwabl
 1 2 3 4 5 6 7 # Example 1: F=SimulCASE1(10) Median1norm(F,200) # Example 2: F=matrix(c(1,0,2,3),nrow=1) Median1norm(F)