DthetaphiTra function

Mid/spr distance between trapezoidal fuzzy numbers

This function calculates the mid/spr 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).

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

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=1/3. 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 trapezoidal fuzzy numbers of the matrix R and the trapezoidal fuzzy numbers of the matrix S.

References

[1] Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications, European Journal of Operational Research 251, pp. 918-929 (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, Dthetaphi

Examples

# Example 1:
F=SimulCASE1(6)
S=SimulCASE1(8)
DthetaphiTra(F,S)

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