Dthetaphi: Mid/spr distance between fuzzy numbers
In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

Description Usage Arguments Details Value Note Author(s) References See Also Examples

This function calculates the mid/spr 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.

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

`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`=1/3. It is the weight of the spread in the mid/spr distance.

See examples

The function returns a matrix of dimension r x s containing the mid/spr distances between the fuzzy numbers of the array R and the fuzzy numbers of the array S .

In case you find (almost surely existing) bugs or have recommendations for improving the functions comments are welcome to the above mentioned mail addresses.

Asun Lubiano <lubiano@uniovi.es>, Sara de la Rosa de Saa <rosasara@uniovi.es>

[1] Blanco-Fernandez, A.; Casals, R.M.; Colubi, A.; Corral, N.; Garcia-Barzana, M.; Gil, M.A.; Gonzalez-Rodriguez, G.; Lopez, M.T.; Lubiano, M.A.; Montenegro, M.; Ramos-Guajardo, A.B.; de la Rosa de Saa, S.; Sinova, B.: Random fuzzy sets: A mathematical tool to develop statistical fuzzy data analysis, Iranian Journal on Fuzzy Systems 10(2), pp. 1-28 (2013)

checking, DthetaphiTra

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

# Example 2:
F=SimulCASE1(10)
S=SimulCASE1(10)
Dthetaphi(F,S,2,1,1/3)

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