This chapter studies and analyzes the characteristics of output versus input values in a neural network when the boundaries of the sets constituting the input and output entities are not precise; that is, when they are fuzzy. In order to develop a meaningful functional representation of the fuzzy-output versus fuzzy-input relation pertinent to a neural network, it is precursive to consider the prevailing strategies adopted in modeling the non-fuzzy, neural input-output relation relevant to crisp sets of inputs and output values. Fuzzy attributes follow the multivalue logic—a logic that builds gray truth into complex schemes of formal reasoning. Such a logic refers to a fuzzy system or mapping from input-to-output that depends on a set of fuzzy rules. Accordingly, a fuzzy set can be defined mathematically by assigning to each possible individual in the universe of discourse a value representing its grade of membership in the fuzzy set.