Median1norm:

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 \(\alpha\)-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

Median1norm(F, nl = 101)

Arguments

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).

positive integer, by default nl=101. It indicates the number of desired \(\alpha\)-levels for characterizing the 1-norm median.

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 \(\alpha\)-levels and 3 the number of columns of the array: the first column will be the \(\alpha\)-levels, the second one their infimum values and the third one their supremum values.

Details

See examples

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)

Examples

Run this code

# Example 1:
F=SimulCASE1(10)
Median1norm(F,200)

# Example 2:
F=matrix(c(1,0,2,3),nrow=1)
Median1norm(F)

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