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

## Description

Computes a fuzzy inference test by the traditional fuzzy confidence intervals

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```Fuzzy.CI.test( 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, plot = TRUE ) ```

## 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 ≤ 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. `plot` a logical rule "TRUE" or "FALSE" for defining whether to plot the corresponding graphs or not.

## 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``` ```H0 <- TriangularFuzzyNumber(2.9,3,3.1) H1 <- TriangularFuzzyNumber(3,3,5) res <- Fuzzy.CI.test(type = 0, H0, H1, t = TriangularFuzzyNumber(0.8,1.80,2.80), s.d = 0.79, n = 10, sig = 0.05, distribution = "normal", distance.type="GSGD") ```

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