# Rho1: 1-norm distance between fuzzy numbers In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

## Description

This function calculates the 1-norm distance between the fuzzy numbers contained in two arrays, which should be given in the desired format. For this, the function first checks if the input arrays R and S are in the correct form (tested by checking) and if the α-levels of all fuzzy numbers coincide.

## Usage

 1 Rho1(R, S) 

## Arguments

 R array of dimension nl x 3 x r containing r fuzzy numbers characterized by means of nl α-levels each. The function first calls checking to check if the array R has the correct format. Moreover, the α-levels of the array R should coincide with the ones of the array S (the function checks this condition). S array of dimension nl x 3 x s containing s fuzzy numbers characterized by means of nl α-levels each. The function first calls checking to check if the array S has the correct format. Moreover, the α-levels of the array S should coincide with the ones of the array R (the function checks this condition).

See examples

## Value

The function returns a matrix of dimension r x s containing the 1-norm distances between the fuzzy numbers of the array R and the fuzzy numbers of the array S .

## 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] Diamond, P.; Kloeden, P.: Metric spaces of fuzzy sets, Fuzzy Sets Syst. 35, pp. 241-249 (1990)

checking, Rho1Tra
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 # Example 1: F=SimulCASE1(4) S=SimulCASE1(5) F=TransfTra(F) S=TransfTra(S) Rho1(F,S) # Example 2: F=SimulCASE1(4) S=SimulCASE1(5) S=TransfTra(S) Rho1(F,S) # Example 3: F=SimulCASE1(4) S=SimulCASE1(5) F=TransfTra(F) S=TransfTra(S,10) Rho1(F,S)