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

In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

Description

This function calculates the (\varphi,θ)-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 α-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 α-levels each. The function first calls checking to check if the array R has the correct format. Moreover, the α-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 α-levels each. The function first calls checking to check if the array S has the correct format. Moreover, the α-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,θ)-wabl/ldev/rdev distance.

Details

See examples

Value

The function returns a matrix of dimension r x s containing the (\varphi,θ)-wabl/ldev/rdev 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] 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)

Example output

          [,1]     [,2]     [,3]     [,4]
[1,] 5.7334102 7.148418 3.752110 1.084761
[2,] 0.7843838 0.988634 2.584992 5.084093
[3,] 1.1112307 2.502965 3.074500 4.676695
[1] "each fuzzy number should be characterized by means of a matrix with 3 columns: the first column will be the alpha-levels, the second one their infimum values and the third one their supremum values"
[1] "each fuzzy number should be characterized by means of a matrix with 3 columns: the first column will be the alpha-levels, the second one their infimum values and the third one their supremum values"
[1] "the fuzzy numbers of the two arrays must have the same alpha-levels"
Warning message:
In R[, 1, 1] == S[, 1, 1] :
  longer object length is not a multiple of shorter object length

FuzzyStatTra documentation built on May 2, 2019, 10:59 a.m.