# EM.Fuzzy-package: EM Algorithm for Maximum Likelihood Estimation by Non-Precise... In EM.Fuzzy: 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).

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ``` 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 documentation built on May 1, 2019, 11:01 p.m.