distance {FuzzySTs}

Calculates a distance between fuzzy numbers

Description

Calculates a distance between fuzzy numbers

Usage

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 \le 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

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