Thierry Denoeux
Thierry Denoeux
Thierry Denoeux
Thierry Denoeux
Thierry Denoeux

Site Tools


This is an old revision of the document!

Fuzzy EM (E2M) algorithm

A method for estimating the parameters in a parametric statistical model when the observations are fuzzy and are assumed to be related to underlying crisp realizations of a random sample. This method is based on maximizing the observed-data likelihood defined as the probability of the fuzzy data.

The toolbox provides functions for the following problems:

  • normal mean and variance estimation from trapezoidal fuzzy data;
  • multiple linear regression with crisp inputs and trapezoidal fuzzy outputs;
  • univariate finite normal mixture estimation from trapezoidal fuzzy data.


  1. T. Denoeux. Maximum likelihood estimation from fuzzy data using the EM algorithm. Fuzzy Sets and Systems, accepted for publication, 2011, doi:10.1016/j.fss.2011.05.022. pdf


User Tools