FzMEBN: Toward a General Formalism of Fuzzy Multi-Entity Bayesian Networks for Representing and Reasoning with Uncertain Knowledge

Good representing and reasoning with uncertainty is a topic of growing interest within the community of artificial intelligence (AI). In this context, the Multi-Entity Bayesian Networks (MEBNs) are proposed as a candidate solution. It’s a powerful tool based on the first order logic expressiveness. Furthermore, in the last decade they have shown its effectiveness in various complex and uncertainty-rich domains. However, in most cases the random variables are vague or imprecise by nature, to deal with this problem; we have to extend the standard Multi-Entity Bayesian Networks to improve their capabilities for good representing and reasoning with uncertainty. This paper details a promising solution based on fuzzy logic; it permits to overcome the weaknesses of classical Multi-Entity Bayesian networks. In addition, we have proposed a general process for the inference task. This process contains four steps, (1) Generating a Fuzzy Situation Specific Bayesian Networks, (2) Computing fuzzy evidence, (3) Adding virtual nodes, and (4) finally, the fuzzy probabilistic inference step. Our process is based on the virtual evidence method in order to incorporate the fuzzy evidence in probabilistic inference, moreover, approximate or exact algorithms can be used, and this choice of inference type depends to the contribution of the domain expert and the complexity of the problem. Illustrative examples taken from the literatures are considered to show potential applicability of our extended MEBN.