# On fuzzy analysis of variance In FuzzySTs: Fuzzy Statistical Tools

detach(data)


## FTukeyHSD(): Calculates the Tukey HSD test corresponding to the fuzzy response variable

In the case of the Mult-FMANOVA model performed by the distance method, the function FuzzySTs::FTukeyHSD() calculates the Tukey HSD test applied on the mean of the fuzzy response variable related to the different factor levels. We have to remind that this test is done by variable, and not for the complete model. This function returns a table of comparisons of means of the different levels of a given factor, two by two. The table contains the means of populations, the lower and upper bounds of the confidence intervals, and their p-values.

# Calculation of the Tukey HSD test for the fuzzy variable X1
mat <- matrix(c(2,2,1,1,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,2,3,4,4,3,1,2,5,4,4,3),ncol=3)
data <- data.frame(mat)
MF131 <- TrapezoidalFuzzyNumber(0,1,1,2)
MF132 <- TrapezoidalFuzzyNumber(1,2,2,3)
MF133 <- TrapezoidalFuzzyNumber(2,3,3,4)
MF134 <- TrapezoidalFuzzyNumber(3,4,4,5)
MF135 <- TrapezoidalFuzzyNumber(4,5,5,6)
PA13 <- c(1,2,3,4,5); mi <- 1; si <- 3
Yfuzz <- FUZZ(data,1,3,PA13)

attach(data)
formula <- X3 ~ X1 + X2
res <- FMANOVA(formula, data, Yfuzz, method = "distance", distance.type = "wabl")
FTukeyHSD(res, "X1")[[1]]

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## Ftests(): Calculates multiple tests corresponding to the fuzzy response variable

In the case of the Mult-FMANOVA model performed by the distance method, this function FuzzySTs::Ftests() calculates multiple indicators of the comparison between the means of the different level factors. We draw the attention that these indicators are constructed on the sums of squares related to the complete model. Thus, no particular factors are specifically involved. This function returns a table of the following different indicators "Wilks","F-Wilks", "Hotelling-Lawley trace" and "Pillai Trace".

# Calculation of the Ftests of the following example
mat <- matrix(c(2,2,1,1,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,2,3,4,4,3,1,2,5,4,4,3),ncol=3)
data <- data.frame(mat)
MF131 <- TrapezoidalFuzzyNumber(0,1,1,2)
MF132 <- TrapezoidalFuzzyNumber(1,2,2,3)
MF133 <- TrapezoidalFuzzyNumber(2,3,3,4)
MF134 <- TrapezoidalFuzzyNumber(3,4,4,5)
MF135 <- TrapezoidalFuzzyNumber(4,5,5,6)
PA13 <- c(1,2,3,4,5); mi <- 1; si <- 3
Yfuzz <- FUZZ(data,1,3,PA13)

attach(data)
formula <- X3 ~ X1 + X2
res <- FMANOVA(formula, data, Yfuzz, method = "distance", distance.type = "wabl")
Ftests(res)

detach(data)


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