EM.Fuzzy-package {EM.Fuzzy} | R Documentation |

## EM Algorithm for Maximum Likelihood Estimation by Non-Precise Information

### Description

The main goal of this package is easy estimation of the unknown parameter of a continues distribution by EM algorithm where the observed data are fuzzy rather than crisp. This package contains two major functions: (1) the function `EM.Triangular`

works by Triangular Fuzzy Numbers (TFNs), and (2) the function `EM.Trapezoidal`

works by Trapezoidal Fuzzy Numbers (TrFNs).

### Author(s)

Abbas Parchami

### References

Denoeux, T. (2011) Maximum likelihood estimation from fuzzy data using the EM algorithm, Fuzzy Sets and Systems 183, 72-91.

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

Gagolewski, M., Caha, J. (2015) A guide to the FuzzyNumbers package for R (FuzzyNumbers version 0.4-1) http://FuzzyNumbers.rexamine.com

### Examples

```
library(FuzzyNumbers)
library(DISTRIB, warn.conflicts = FALSE)
# Let us we are going to estimation the unknown mean of Normal population with known variance
# (e.g, sd(X) = 0.5) on the basis of 11 trapezoidal fuzzy numbers (which we simulate them in
# bellow for simplification).
n = 11
set.seed(1000)
c1 = rnorm(n, 10,.5)
c2 = rnorm(n, 10,.5)
for(i in 1:n) {if (c1[i] > c2[i]) { zarf <- c1[i]; c1[i] <- c2[i]; c2[i] <- zarf }}
round(c1,3); round(c2,3)
c1 <= c2
l = runif(n, 0,1); round(l,3)
u = runif(n, 0,1); round(u,3)
EM.Trapezoidal(T.dist="norm", T.dist.par=c(NA,0.5), par.space=c(-5,30), c1, c2, l, u,
start=4, ebs=.0001, fig=2)
```

*EM.Fuzzy*version 1.0 Index]