DwablphiTra function

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

This function calculates the $(\varphi,\theta)$-wabl/ldev/rdev distance between the trapezoidal fuzzy numbers contained in two matrixes, which should be given in the desired format. For this, the function first checks if the input matrixes R and S are in the correct form (tested by checkingTra).

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

Arguments

• R: matrix of dimension r x 4 containing r trapezoidal fuzzy numbers characterized by their four values inf0,inf1,sup1,sup0. The function first calls checkingTra to check if the matrix R has the correct format.
• S: matrix of dimension s x 4 containing s trapezoidal fuzzy numbers characterized by their four values inf0,inf1,sup1,sup0. The function first calls checkingTra to check if the matrix S has the correct format.
• 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 trapezoidal fuzzy numbers of the matrix R and the trapezoidal fuzzy numbers of the matrix 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

checkingTra, Dwablphi, Wablphi

Examples

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

# Example 2:
F=matrix(c(1,1,0,2,3,4,5,6),nrow=2)
S=SimulCASE1(8)
DwablphiTra(F,S)