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.

References:

1. T. Denoeux. Maximum likelihood from evidential data: an extension of the EM algorithm. In C. Borgelt et al. (Eds), Combining soft computing and statistical methods in data analysis (Proceedings of SMPS 2010, Oviedo, Spain, September 28 - October 1, 2010), Advances in Intelligent and Soft Computing, pages 181-188, Springer, 2010. pdf
2. T. Denoeux, Maximum likelihood estimation from Uncertain Data in the Belief Function Framework, IEEE Transactions on Knowledge and Data Engineering (to appear), 2011.

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