In this chapter, we introduce some of the basic themes of this work. We begin with some background material on artificial intelligence and the paradigms of connectionism and symbolism. This is followed by a very brief review of artificial neural networks (ANNs) and fuzzy rule-based systems (FRBs). This sets the stage for the presentation of the main tool developed in this work, the fuzzy all-permutations rule-base (FARB). This is an FRB with a special form. This form guarantees that the input-output mapping of the FARB is mathematically equivalent to that of an ANN. This provides a new synergy between the learning-from-examples ability of ANNs and the high-level symbolic information processing of FRBs.