document: Mathematical fundamentals of constructing fuzzy Bayesian inference techniques Problems and an associated technique for developing a Bayesian approach to decision-making in the case of fuzzy data are presented . The concept of fuzzy and pseudofuzzy quantities is introduced and main operations with pseudofuzzy quantities are considered . The basic relationships and the principal concepts of the Bayesian decision procedure based on the modus-ponens rule are proposed . Some problems concerned with the practical realization of the fuzzy Bayesian method are considered
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