FuzzyStatTra (version 1.0)

Dwablphi:

Description

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.

Usage

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.

Value

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 .

Details

See examples

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)

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)