FuzzySTs (version 0.4)

optimal.distance: Calculates the optimal distance between two fuzzy numbers according to the chosen type

Description

Calculates the optimal distance between two fuzzy numbers according to the chosen type

Usage

optimal.distance(
  X,
  Y,
  type = "DSGD.G",
  i = 1,
  j = 1,
  theta = 1/3,
  thetas = 1,
  p = 2,
  q = 0.5,
  breakpoints = 100
)

Value

A numerical value.

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.

Examples

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