FuzzySTs (version 0.3)

Fuzzy.decisions.ML: Computes the fuzzy decisions of a fuzzy inference test by the fuzzy confidence intervals by the likelihood method

Description

Computes the fuzzy decisions of a fuzzy inference test by the fuzzy confidence intervals by the likelihood method

Usage

Fuzzy.decisions.ML(
  data.fuzzified,
  H0,
  H1,
  t,
  coef.boot,
  mu = NA,
  sigma = NA,
  sig,
  distribution,
  distance.type = "DSGD",
  i = 1,
  j = 1,
  theta = 1/3,
  thetas = 1,
  p = 2,
  q = 0.5,
  breakpoints = 100,
  step = 0.05,
  margin = c(5, 5),
  plot = FALSE
)

Value

Returns a list composed by the arguments, the fuzzy confidence intervals, the fuzzy decisions, the defuzzified values and the decision made.

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.

H0

a trapezoidal or a triangular fuzzy number representing the fuzzy null hypothesis.

H1

a trapezoidal or a triangular fuzzy number representing the fuzzy alternative hypothesis.

t

a given numerical or fuzzy type parameter of the distribution.

coef.boot

a decimal representing the 1-sig-quantile of the bootstrap distribution of LR.

mu

if the mean of the normal distribution is known, mu should be a numerical value. Otherwise, the argument mu is fixed to NA.

sigma

if the standard deviation of the normal distribution is known, sigma should be a numerical value. Otherwise, the argument sigma is fixed to NA.

sig

a numerical value representing the significance level of the test.

distribution

a distribution chosen between "normal", "poisson", "Student" or "Logistic".

distance.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, p 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.

step

a numerical value fixed to 0.05, defining the step of iterations on the interval [t-5; t+5].

margin

an optional numerical couple of values fixed to [5; 5], representing the range of calculations around the parameter t.

plot

fixed by default to "FALSE". plot="FALSE" if a plot of the fuzzy number is not 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(2,3,3,4)
PA11 <- c(1,2,3)
data.fuzzified <- FUZZ(data,mi=1,si=1,PA=PA11)
H0 <- alphacut(TriangularFuzzyNumber(2.9,3,3.1), seq(0,1, 0.01))
H1 <- alphacut(TriangularFuzzyNumber(3,3,5), seq(0,1,0.01))
t <- alphacut(TriangularFuzzyNumber(0.8,1.80,2.80), seq(0,1,0.01))
coef.boot <- 3.470085
res <- Fuzzy.decisions.ML(data.fuzzified, H0, H1, t = t, coef.boot = coef.boot, 
sigma = 0.79, sig = 0.05, distribution = "normal", distance.type = "GSGD")