ANOVA.TFNs (version 1.0)

ANOVA.TFNs-package: ANOVA.TFNs

Description

Long formulas and complex computations are two major disadvantages of the extended ANOVA approaches for fuzzy data. The applied users/practitioners of fuzzy ANOVA can overcome to these challenges/disadvantages, by using package ANOVA.TFNs when the observed data for ANOVA test are triangular fuzzy numbers. The most important functions in package ANOVA.TFNs is FANOVA. Using FANOVA is easy since after import fuzzy observation (with format FANOVA.Data), the FANOVA function easily export: (1) draw separately the membership functions of TFNs for each population in one figure, (2) FANOVA Table (which include details of fuzzy ANOVA based on Triangular fuzzy data, (3) the observed value of the FANOVA test statistics, (4) the p-value of FANOVA test, and (5) FANOVA test result at the considered significance level.

Details

The inputted data for FANOVA test must be in a special format which we named it FANOVA.Data format and some of inputted parameters in several functions of this package (such as means.vec, FANOVA, plotTFNs, crisp.Data, f.fuzzy and ...) must be in FANOVA.Data format. In fact, the FANOVA.Data is a matrix with \(dim=c(n,4)\) which can be created/simulated by following two steps:

Step 1 (saving/creating TFNs of i-th population in a matrix with \( dim=c(n_i,3))\): Save Triangular Fuzzy Numbers (TFNs) for FANOVA test in length(n) matrix and input each TFN in one row of them such that: 1st column is for Cores of TFNs (with col.name="C"), 2nd column is for Left spreads of TFNs (with col.name="L"), and 3nd column is for Right spreads of TFNs (with col.name="R").

Step 2 (Combine all population data in a matrix with \( dim=c(n,4))\): Put The created matrixes in Step 1, top of each other to create a matrix with \(dim=c(n,4)\) such that: n=sum(n_i), its 1st column is the Core of TFNs (with col.name="C"), its 2nd and 3nd columns are the Left and Right spreads of TFNs (with col.name="L" and col.name="R") respectively, and its 4nd column is the factor which shows the population number for each row (with col.name="factor").

See Example 1 in bellow.

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 (input TFNs in \code{FANOVA.Data} format)
data(Data)
head(Data)
Data[,"R"]
Data[,"C"][Data[,"factor"]==2]  
# }
# NOT RUN {
 # Or Data[,"C"][Data[,4]==2] 
# }
# NOT RUN {

## Example 2:  
FANOVA( Data, m=2, sig.level=0.1 )


## Example 3: 
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))

# }