Description Author(s) References Examples
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
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
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)
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