The Bayes Theorem For Fuzzy Interval-valued Measures

Recent years, Bayesian statistics has been made great progress in theoretical research and applied research. Since hypothesis testing theory is one of the basic contents of statistics, its fundamental task is the deduction of rejection or acceptation under the inference for some hypotheses of the population characteristics based on the sample data with randomness. Randomness is that each event of the event set with a certain probability demonstrates uncertainty.Fuzziness introducing to classical statistical inference is different from another uncertainty in randomness. It is an important research in statistics in recent years. Based on the Bayesian statistical decision, the prior information and sample information are fuzzed, and the continuous fuzzy Bayesian formula of population situation is derived, so a way of the effective utilization of fuzzy priori information and fuzzy sample information is provided. Then the Bayesian formula of fuzzy events is studied, the classical Bayesian method is generalized, and a numerical example is illustrated to show the effectiveness of the method. Finally, interval-valued measure Bayesian formula is deduced according to the classical Bayesian formula; What’s more, the fuzzy interval-valued measure Bayesian formula is introduced for further extension, which provides a theoretical basis for statistics method of interval-valued data.