Reference: Drakopoulos, J. A. Sigmoidal Theory. Knowledge Systems Laboratory, May, 1994.
Abstract: Sigmoidal theory is a new theory that defines and analyzes a new family of functions called {\em sigmoidal functions.\/} A number of theorems proved show that there is an infinite number of classes of sigmoidal functions and provide us with a method of constructing those classes. The applications of sigmoidal functions range from fuzzy sets to neural networks and pattern recognition. Fuzzy sets, in particular, are expected to be benefited the most by the use of sigmoidal functions in modeling fuzzy membership. The formalization of sigmoidal functions here is expected to increase the interest in them and result in a number of new applications.
Full paper available as ps.