# distance: Calculates a distance between fuzzy numbers In FuzzySTs: Fuzzy Statistical Tools

## Description

Calculates a distance between fuzzy numbers

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```distance( X, Y, type, i = 1, j = 1, theta = 1/3, thetas = 1, p = 2, q = 0.5, breakpoints = 100 ) ```

## Arguments

 `X` a fuzzy number. `Y` a fuzzy number. `type` type of distance chosen from the family of distances. The different choices are given by: "Rho1", "Rho2", "Bertoluzza", "Rhop", "Delta.pq", "Mid/Spr", "wabl", "DSGD", "DSGD.G", "GSGD". `i` parameter of the density function of the Beta distribution, fixed by default to i = 1. `j` parameter of the density function of the Beta distribution, fixed by default to j = 1. `theta` a numerical value between 0 and 1, representing a weighting parameter. By default, theta is fixed to 1/3 referring to the Lebesgue space. This measure is used in the calculations of the following distances: d_Bertoluzza, d_mid/spr and d_phi-wabl/ldev/rdev. `thetas` a decimal value between 0 and 1, representing the weight given to the shape of the fuzzy number. By default, thetas is fixed to 1. This parameter is used in the calculations of the d_theta star and the d_GSGD distances. `p` a positive integer such that 1 ≤ p < infinity, referring to the parameter of the Rho_p and Delta_pq. `q` a decimal value between 0 and 1, referring to the parameter of the metric Delta_pq. `breakpoints` a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default.

## Value

A numerical value.

## Examples

 ```1 2 3 4``` ```X <- TrapezoidalFuzzyNumber(1,2,3,4) Y <- TrapezoidalFuzzyNumber(4,5,6,7) distance(X, Y, type = "DSGD.G") distance(X, Y, type = "GSGD") ```

FuzzySTs documentation built on Nov. 23, 2020, 5:11 p.m.