Soft Computing is the fusion of methodologies that were designed to model and enable solutions to real world problems, which are not modeled, or too difficult to model, mathematically. These problems are typically associated with fuzzy, complex, and dynamical systems, with uncertain parameters. These systems are the ones that model the real world and are of most interest to the modern science. Among the methodologies of Soft Computing, two seem to, mistakenly, be considered alternatives, namely, Fuzzy Computing and Probabilistic Computing. The fusion of methodologies that characterizes Soft Computing suggests the complementarity, rather than the comparison, of the two systems. This dissertation proposes a model for the integration of the two paradigms to solve problems of fuzzy, complex, dynamical systems in which one field cannot solve alone. However, the study of Fuzzy Computing and Probabilistic Computing revealed flaws in both systems that may lead to erroneous and misleading conclusions about the results of their applications. On the Fuzzy Computing side, this dissertation addresses the violation of the Law of Excluded Middle by Fuzzy Set Theory as a non-natural feature of the theory and proposes an extension of the theory to fix the deficiency. The dissertation also identifies the possible erroneous computations that may result from applying the crisp techniques of Probability Theory to fuzzy and complex systems. For a solution, the dissertation initiates the idea of Soft Probability, where a model for computing probabilities of fuzzy systems and events is constructed. Quality of Service Networking is an example of the class of complex, fuzzy, and dynamical systems with uncertain parameters, which Soft Computing is intended to model and compute. The term Quality of Service is a fuzzy term. Its measures are typically fuzzy linguistic hedges. The uncertainty associated with the network state information is inevitable in terms of, both, fuzziness and randomness. Therefore, the integration of Fuzzy and Probabilistic Computing ought to be an ideal approach to the implementation of Quality of Service networks. This dissertation proposes a model for applying the integration of fuzzy and probabilistic techniques for building intelligent adaptive communication systems.
