Rho1 {FuzzyStatTra}

1-norm distance between 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 \alpha-levels of all fuzzy numbers coincide.

Usage

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

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 <[e-mail]>, Sara de la Rosa de Saa <[e-mail]>

References

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

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)