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

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```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 ) ```

## 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. `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.

## Value

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```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 ```

FuzzySTs documentation built on Nov. 23, 2020, 5:11 p.m.