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

This function calculates the scale measure Average Distance Deviation (ADD) for a matrix of trapezoidal fuzzy numbers `F`

with respect to a fuzzy number `U`

. The employed metric in the calculation can be the 1-norm distance, the mid/spr distance or the *(\varphi,θ)*-wabl/ldev/rdev distance. The function first checks if the input matrix `F`

is given in the correct form (tested by `checkingTra`

) and also the input fuzzy number `U`

(tested by `checking`

or `checkingTra`

).

1 |

`F` |
matrix of dimension |

`U` |
can be a matrix of dimension |

`type` |
number 1, 2 or 3: if |

`a` |
number >0, by default |

`b` |
number >0, by default |

`theta` |
number >0, by default |

See examples

The function returns the scale measure ADD, which is a real number.

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] De la Rosa de Saa, S.; Lubiano M.A.; Sinova, B.; Filzmoser, P.: *Robust scale estimators for fuzzy data*, Advances in Data Analysis and Classification, pp. 1-28 (2015)

`checkingTra`

, `checking`

, `TransfTra`

, `Rho1Tra`

, `Rho1`

, `DthetaphiTra`

, `Dthetaphi`

, `DwablphiTra`

, `Dwablphi`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
# Example 1:
F=SimulCASE1(10)
U=Mean(F)
ADD(F,U,1)
# Example 2:
F=SimulCASE1(100)
U=Median1norm(F)
ADD(F,U,2,2,1,1)
# Example 3:
F=SimulCASE1(100)
U=matrix(c(1,2,3,2),nrow=1)
ADD(F,U,1)
# Example 4:
F=matrix(1:4,nrow=2)
U=matrix(1:4,nrow=1)
ADD(F,U,3,1,1,1)
``` |

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