Dthetaphi function

Mid/spr distance between fuzzy numbers

This function calculates the mid/spr 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.

Dthetaphi(R, S, a = 1, b = 1, theta = 1/3)

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).
• a: number >0, by default a=1. It is the first parameter of a beta distribution which corresponds to a weighting measure on [0,1].
• b: number >0, by default b=1. It is the second parameter of a beta distribution which corresponds to a weighting measure on [0,1].
• theta: number >0, by default theta=1/3. It is the weight of the spread in the mid/spr distance.

Details

See examples

Returns

The function returns a matrix of dimension r x s containing the mid/spr distances between the fuzzy numbers of the array R and the fuzzy numbers of the array S .

References

[1] Blanco-Fernandez, A.; Casals, R.M.; Colubi, A.; Corral, N.; Garcia-Barzana, M.; Gil, M.A.; Gonzalez-Rodriguez, G.; Lopez, M.T.; Lubiano, M.A.; Montenegro, M.; Ramos-Guajardo, A.B.; de la Rosa de Saa, S.; Sinova, B.: Random fuzzy sets: A mathematical tool to develop statistical fuzzy data analysis, Iranian Journal on Fuzzy Systems 10(2), pp. 1-28 (2013)

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, DthetaphiTra

Examples

# Example 1:
F=SimulCASE1(10)
S=SimulCASE1(20)
F=TransfTra(F)
S=TransfTra(S)
Dthetaphi(F,S,1,5,1)

# Example 2:
F=SimulCASE1(10)
S=SimulCASE1(10)
Dthetaphi(F,S,2,1,1/3)

# Example 3:
F=SimulCASE1(10)
S=SimulCASE1(10)
F=TransfTra(F)
S=TransfTra(S,50)
Dthetaphi(F,S,2,1,1)