Geodesic
Fuzzy Bayesian inferences
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 1, pp. 8-12.

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We consider generalization of Bayesian theorem for the cases with fuzzy observations. It will be considered one of the forms of fuzzy Bayesian theorem introduced by Viertl. One can observe that it cannot be used as a generalization of ordinary Bayesian theorem with the form of likelihood function. We introduce other types of likelihood function satisfying some definite conditions.
Keywords: fuzzy statistics, Bayesian theorem, fuzzy random variables. 
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V. G. Bardakhchyan. Fuzzy Bayesian inferences. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 1, pp. 8-12. http://geodesic.mathdoc.fr/item/UZERU_2017_51_1_a1/

[1] J. G. Klirl, B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall PTR, 1995 | MR

[2] R. Viertl Statistical Methods for Fuzzy Data, Wiley, Chichester, 2011 | MR | Zbl

[3] R. Viertl, O. Sunanta, “Fuzzy Bayesian Inference.”, METRON, 71:3 (2013), 207–216 | DOI | MR | Zbl

[4] J. Buckley, Fuzzy Probability and Statistics, Berlin, Heidleberg, 2006.

[5] C.C. Yang, “Fuzzy Bayesian Inference”, IEEE International Conference, Proceeding of Systems, Man and Cybernetics, 3, 1997, 2707–2712

[6] O. Osoba, S.Miataim, B. Kosko, “Bayesian Inference with Adaptive Fuzzy Priors and Likelihoods”, IEEE Transactions on Systems, Man and Cybernetics, 41:5 (2011), 1183–1197 | DOI

[7] D.B. Owen, “A Table of Normal Integrals”, Communication in Statistics – Simulation and Computation, 9:4 (1980), 389–419 | DOI | MR

[8] M. Sugeno, Theory of Fuzzy Integrals and Its Applications, PhD Thesis, Tokyo Institute of Technology, 1974