FuzzySTs (version 0.3)

Fuzzy.decisions: Computes the fuzzy decisions of a fuzzy inference test by the traditional fuzzy confidence intervals

Description

Computes the fuzzy decisions of a fuzzy inference test by the traditional fuzzy confidence intervals

Usage

Fuzzy.decisions(
  type,
  H0,
  H1,
  t,
  s.d,
  n,
  sig,
  distribution,
  distance.type = "DSGD",
  i = 1,
  j = 1,
  theta = 1/3,
  thetas = 1,
  p = 2,
  q = 0.5,
  breakpoints = 100
)

Value

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

Arguments

type

a category betwenn "0", "1" and "2". The category "0" refers to a bilateral test, the category "1" for a lower unilateral one, and "2" for an upper unilateral test.

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.

s.d

a numerical value for the standard deviation of the distribution.

n

the total number of observations of the data set.

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.

Examples

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))
res <- Fuzzy.decisions(type = 0, H0, H1, t = t, s.d = 0.79, n = 10, sig = 0.05,
distribution = "normal", distance.type = "GSGD")