Median1norm function

1-norm median of a trapezoidal fuzzy sample

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).

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 $\alpha$-levels for characterizing the 1-norm median.

Details

See examples

Returns

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.

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)

Author(s)

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

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.

See Also

checkingTra, TransfTra, Medianwabl

Examples

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

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