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

## Description

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.

## Usage

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

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

See examples

## Value

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 .

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

## References

[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
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 # 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)