EM algorithm based on fuzzy observations

Document Type : Original Article

Author

20.1001.1.27174409.1397.1.2.3.6/DOR

Abstract

The EM algorithm is a powerful tool for estimating maximum accuracy based on incomplete data and has been discussed in most statistical inference books. Here, the meaning of the word "incomplete" is general, and in different situations it can mean a variety of meanings (such as missing data, interval data, censored observations, and the like).
This paper introduces a new application of the EM algorithm in which incomplete data refers to inaccurate / ambiguous / fuzzy data. Based on this type of ambiguous data, in this paper, the maximum likelihood estimate of the exponential distribution parameter is calculated using the EM algorithm in the form of a numerical example, and this example can be used to understand the material and also use the EM algorithm in the examples / modes. More complex, useful for graduate students based on fuzzy observations

Keywords

References

[1] A. P. Dempster, N. M. Laird and D. B. Rubin, Maximum Likelihood from Incomplete Data via the EM Algorithm, Journal of the Royal Statistical Society 39(1977), 1-38.
 
[2] T. Denoeux, Maximum likelihood estimation from fuzzy data using the EM algorithm, Fuzzy Sets and Systems 183(2011), 72-91.
 
[3] K. Knight, Mathematical Statistics, New York, Chapman & Hall, (2000).
 
[4] R. Pourmousa, On truncated measures of income inequality from a fuzzy perspective, Iranian Journal of Fuzzy Systems 15(2018), 123-137.
 
[5] L. A. Zadeh, Probability measures of fuzzy events, J. Math. Anal. Appl, 23(1968), 421-427.

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History

  • Receive Date: 16 June 2018
  • Accept Date: 16 April 2019

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