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

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`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 |

`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.

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
``` |

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