ANOVA.TFNs (version 1.0)

FANOVA: Fuzzy ANOVA Test

Description

This function is the main function of package ANOVA.TFNs it can easily test one-way Analysis of Variance based on Triangular Fuzzy observation on the basis of m=1,2,3,... by (Parchami et al., 2017, 2018) method.

Usage

FANOVA(Data, m = 1, sig.level = 0.05, fig = TRUE)

Arguments

Data

a matrix with \(dim=c(n, 4)\) and FANOVA.Data format.

m

a positive integer number which related to the weight of distance between two cuts of fuzzy numbers, and its default is m=1. For more details see (Parchami et al., 2017, 2018).

sig.level

the significance level of test with default sig.level=0.05.

fig

a logical argument with default TRUE. If fig=TRUE, the membership functions of inputted fuzzy data will be depicted in a figure as presented in plotTFNs function.

Value

Function FANOVA returned the values:

table

Fuzzy ANOVA Table which contains details of FANOVA based on Triangular fuzzy data

f_ob

The observed value of test statistic in FANOVA test, which sometimes denoted by F-statistic

p_value

The p-value in FANOVA test which is equal to the above tail area of F-statistic

FANOVA_test_result

Final report (Accept/Reject) H_0 at the considered significance level

Details

Function FANOVA compute all needed statistics for Fuzzy ANOVA test which introduced in (Parchami et al., 2018) and is able report the FANOVA table and the p-value of FANOVA test.

References

Gagolewski, M., Caha, J. (2015) FuzzyNumbers Package: Tools to deal with fuzzy numbers in R. R package version 0.4-1, https://cran.r-project.org/web/packages=FuzzyNumbers

A. Parchami, M.R. Nourbakhsh, M. Mashinchi (2017) Analysis of Variance in Uncertain Environments, Complex & Intelligent Systems, Volume 3, Number 3, 189-196, DOI: 10.1007/s40747-017-0046-8

A. Parchami, M. Mashinchi, C. Kahraman (2018) An Implication of Fuzzy ANOVA in Vehicle Battery Manufacturing, Journal of Enterprise Information Management, Preprint.

See Also

FuzzyNumbers

Examples

# NOT RUN {
# Example 1: 

data(Data)
head(Data)

FANOVA( Data )
FANOVA( Data, fig=FALSE )
FANOVA( Data, m=2, sig.level=0.1 )
FANOVA( Data, fig=FALSE  )$p_value
FANOVA( Data, fig=FALSE  )$FANOVA_test_result
FANOVA( Data, fig=FALSE  )[[1]]  
# }
# NOT RUN {
 # Only FANOVA Table 
# }
# NOT RUN {

# Example 2: 
t <- 20
f <-p <- c()

for(i in 1:t){
		 f[i] <- FANOVA(Data, m=i, fig=FALSE)$f_ob
		 p[i] <- FANOVA(Data, m=i, fig=FALSE)$p_value
		 }

par(mfcol=c(2,1))
  plot(1:t, f, main="FANOVA test statistics (f) v.s m (1:20)")
  plot(1:t, p, main="p-value v.s m (1:20)")
par(mfcol=c(1,1))

# }