EM.Fuzzy-package {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).

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)