Rho1 function

1-norm distance between fuzzy numbers

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 $\alpha$-levels of all fuzzy numbers coincide.

Rho1(R, S)

Arguments

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

Details

See examples

Returns

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 .

References

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

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

checking, Rho1Tra

Examples

# 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)