Using the fuzzy version of the pearl's algorithm for environmental risk assessment tasks

In risk assessment, numerous subfactors influence the probabilities of the main factors. These main factors reflect adverse outcomes, which are essential in risk assessment. A Bayesian network can model the entire set of subfactors and their interconnections. To assess the probabilities of all possible states of the main factors (adverse consequences), complete information about the probabilities of all relevant subfactor states in the network nodes must be utilized. This is a typical task of probabilistic inference. The algorithm proposed by J. Pearl is widely used for point estimates of relevant probabilities. However, in many practical problems, including environmental risk assessment, it is not possible to assign crisp probabilities for relevant events due to the lack of sufficient statistical data. In such situations, expert assignment of probabilities is widely used. Uncertainty in expert assessments can be successfully modeled using triangular fuzzy numbers. That is why this article proposes a fuzzy version of this algorithm, which can solve the problem of probabilistic inference on a Bayesian network when the initial probability values are given as triangular fuzzy numbers.