FuzzySTs (version 0.3)

Fuzzy.variance: Calculates the variance by a chosen method: distance, exact or approximation

Description

Calculates the variance by a chosen method: distance, exact or approximation

Usage

Fuzzy.variance(
  data.fuzzified,
  method,
  dist.type = "DSGD",
  i = 1,
  j = 1,
  theta = 1/3,
  thetas = 1,
  p = 2,
  q = 0.5,
  breakpoints = 100,
  int.method = "int.simpson",
  plot = FALSE
)

Value

If the parameter method = "distance", returns a numerical value. If else, returns the numerical \(\alpha\)-cuts of the estimated fuzzy variance.

Arguments

data.fuzzified

a fuzzification matrix constructed by a call to the function FUZZ or the function GFUZZ, or a similar matrix. No NA are allowed.

method

choices are the following: "distance", "exact", "approximation1", "approxi- mation2", "approximation3", "approximation4", "approximation5".

dist.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. By default, p is fixed to 2.

q

a decimal value between 0 and 1, referring to the parameter of the metric Delta_pq. By default, q is fixed to 0.5.

breakpoints

a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default.

int.method

the integration method could be one of the following four methods: "int.0", "int.t", "int.ct" and "int.simpson".

plot

fixed by default to "FALSE". plot="TRUE" if a plot of the fuzzy number is required.

Examples

data <- matrix(c(1,2,3,2,2,1,1,3,1,2),ncol=1) 
MF111 <- TrapezoidalFuzzyNumber(0,1,1,2) 
MF112 <- TrapezoidalFuzzyNumber(1,2,2,3) 
MF113 <- TrapezoidalFuzzyNumber(2,3,3,3) 
PA11 <- c(1,2,3) 
data.fuzzified <- FUZZ(data,mi=1,si=1,PA=PA11) 
Fuzzy.variance(data.fuzzified, method = "approximation5", plot=TRUE) 
Fuzzy.variance(data.fuzzified, method = "distance")