Dwablphi function

$(\varphi,\theta)$-wabl/ldev/rdev distance between fuzzy numbers

This function calculates the $(\varphi,\theta)$-wabl/ldev/rdev 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.

Dwablphi(R, S, a = 1, b = 1, theta = 1)

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. It is the weight of the ldev and rdev in the $(\varphi,\theta)$-wabl/ldev/rdev distance.

Details

See examples

Returns

The function returns a matrix of dimension r x s containing the $(\varphi,\theta)$-wabl/ldev/rdev distances between the fuzzy numbers of the array R and the fuzzy numbers of the array S .

References

[1] Sinova, B.; de la Rosa de Saa, S.; Gil, M.A.: A generalized L1-type metric between fuzzy numbers for an approach to central tendency of fuzzy data, Information Sciences 242, pp. 22-34 (2013)

[2] Sinova, B.; Gil, M.A.; Van Aelst, S.: M-estimates of location for the robust central tendency of fuzzy data, IEEE Transactions on Fuzzy Systems 24(4), pp. 945-956 (2016)

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, DwablphiTra, Wablphi

Examples

# Example 1:
F=SimulCASE1(3)
S=SimulCASE1(4)
F=TransfTra(F)
S=TransfTra(S)
Dwablphi(F,S,2,1,1)

# Example 2:
F=SimulCASE1(10)
S=SimulCASE1(10)
Dwablphi(F,S)

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