A generalized hybrid fuzzy-Bayesian methodology for modeling complex uncertainty

Due to its well understood nature and its ability to model many phenomena in the physical world extremely well, probability theory is the method of choice for dealing with uncertainty in many science and engineering disciplines. However, as a tool for building representative models of complex real world systems, probability theory has a rather recent history which starts with the introduction of Bayesian Networks (BN).;Broadly construed, the BN model of a system is the compact representation of a joint probability distribution of the variables comprising the system. Many complex real-world systems are naturally represented by hybrid models which contain both discrete and continuous variables. However, when it comes to modeling uncertainty and to performing probabilistic inferencing about hybrid systems, what BNs have to offer is quite limited. Although exact inferencing in BNs composed only of discrete variables is well understood, no exact inferencing algorithms exist for general hybrid BNs.;In this thesis we concentrate on the problem of inferencing in Hybrid Bayesian Networks (HBNs). Our focus, hence our contributions are three-fold: theoretical, algorithmic and practical. From a theoretical point of view, we provide a novel framework to implement a hybrid methodology that complements probability theory with Fuzzy Sets to perform exact inferencing with general Hybrid Bayesian Networks that is composed of both discrete and continuous variables with no graph-structural restrictions to model uncertainty in complex systems. From an algorithmic perspective, we provide a suite of inferencing algorithms for general Hybrid Bayesian Networks. The suite includes two new inferencing algorithms for the two different types of Fuzzy-Bayesian Networks introduced in this study. Finally, from a practical perspective, we apply our framework, methodology, and techniques to the task of assessing system safety risk due to the introduction of emergent Unmanned Aircraft Systems (UASs) into the National Airspace System (NAS).