A fuzzy graph evolved by a new adaptive Bayesian framework and its applications in natural hazards

A formal Bayesian approach that uses the Markov chain Monte Carlo method to estimate the uncertainties of natural hazards has attracted significant attention in recent years, and a fuzzy graph can be considered an estimation of the relationship that we want to know in risk systems. However, the challenge with such approaches is to sufficiently consider uncertainty without much prior knowledge and adequate measurement. This paper proposes a new adaptive Bayesian framework that is based on the conventional Bayesian scheme and the optimal information diffusion model to more precisely calculate the conditional probabilities in the fuzzy graph for recognizing relationships and estimating uncertainty in natural disasters with scant data. This methodology is applied to study the relationship between the earthquake's magnitude and the isoseismal area with strong-motion earthquake observations. It is also compared with other techniques, including classic Bayesian regression and artificial neural networks. The results show that the new method achieves better performance than do the main existing methods with incomplete data.