Fuzzy.CI.ML.test: Computes a fuzzy inference test by the fuzzy confidence...
In FuzzySTs: Fuzzy Statistical Tools

Description Usage Arguments Value Examples

View source: R/Fuzzy_test_CI_25102018.R

Computes a fuzzy inference test by the fuzzy confidence intervals method calculated by the Likelihood method

Fuzzy.CI.ML.test(
  data.fuzzified,
  H0,
  H1,
  t,
  mu = NA,
  sigma = NA,
  sig,
  distribution,
  coef.boot,
  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 = TRUE
)

`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.
`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".
`coef.boot`	a decimal representing the 1-sig-quantile of the bootstrap distribution of LR.
`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 ≤ 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.

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

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)
Fmean <- Fuzzy.sample.mean(data.fuzzified)
H0 <- TriangularFuzzyNumber(2.2,2.5,3)
H1 <- TriangularFuzzyNumber(2.5,2.5,5)
coef.boot <- 3.494829
(res <- Fuzzy.CI.ML.test(data.fuzzified, H0, H1, t = Fmean, sigma=0.7888,
coef.boot = coef.boot, sig=0.05, distribution="normal", distance.type="GSGD"))
res$decision