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Possibilistic Bayesian inference based on fuzzy data

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Abstract

A Bayesian approach in the possibilistic environment is introduced, when the available data of the underlying statistical model are fuzzy. In this approach, based on a possibilistic model and a prior possibility distribution, the possibilistic posterior distribution is defined, when the available data are fuzzy. While the probabilistic Bayesian approach is suitable when we have stochastic uncertainty in the underlying model and available information, the proposed possibilistic Bayesian approach is proper when we come across the possibilistic uncertainty which is related to the notions of compatibility and consistency. A few numerical examples and a couple of applied examples in the field of concept learning are presented to illustrate the applicability of the proposed models.

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Acknowledgments

The authors wish to express their thanks to the referees for valuable comments which improved the paper. They would like to thank Professor Radko Mesiar (at Bratislava University of Technology) for reading the manuscript and for his valuable comment and suggestion which is considered in Remark 9. Also, they express their thanks to Dr. M.M. Pedram (at Kharazmi University) for introducing and providing some necessary reference books. The authors would like to acknowledge the financial support of University of Tehran for this research under grant number 30005/1/01.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, Iran

    Mohsen Arefi

  2. Faculty of Engineering Science, College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran

    S. Mahmoud Taheri

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  1. Mohsen Arefi
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  2. S. Mahmoud Taheri
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Correspondence to S. Mahmoud Taheri.

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Arefi, M., Taheri, S.M. Possibilistic Bayesian inference based on fuzzy data. Int. J. Mach. Learn. & Cyber. 7, 753–763 (2016). https://doi.org/10.1007/s13042-014-0291-8

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