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In this book we pursued the challenge posed by the need to tame uncertainty in the context of medical and epidemiological problems. The fact that epidemiology deals with population of individuals leads to uncertainties of different natures. In fact, much ink has been spent on the speculations about the competitive or complementary role of probability and fuzzy logic in dealing with uncertainty. We are fully convinced that both disciplines address complementary dimensions of uncertainty. The success of applied probability theory in describing sampling variations and model specification in epidemiological problems is undeniable. Yet, fuzzy logic can be an undispensible tool to address vagueness related to intended meaning or linguistic uncertainty. As thoroughly discussed along this book, we believe that they can be seen as subsets of a more general logic. Paraconsistent logic, which in some way generalizes the non-binary properties of fuzzy logic, has been proposed as an appropriate candidate (Sylvan & Abe, 1996; Batens et al., 2000; Abe, 2004; Abe et al., 2005), particularly when combined with neural network structures. More recently, the Neutrosophic logic is appearing as a promise of a new powerful approach with great applicability, due to its flexibility and its connection with fuzzy sets theory (Wang et al., 2005; Kandasamy & Smarandache, 2005).