Mathematical Modeling of Natural Phenomena: A Fuzzy Logic Approach

In many fields of science human observers have provided verbal descriptions and explanations of various systems. A formal mathematical model is indispensable when we wish to rigorously analyze these systems. In this chapter, we survey some recent results on transforming verbal descriptions into mathematical models using fuzzy modeling. This is a simple and direct approach that offers a unique advantage–the close relationship between the verbal description and the mathematical model can be used to verify the validity of the verbal explanation suggested by the observer. We review two applications of this approach from the field of ethology: the territorial behavior of the fish and the orientation to light of a flat worm. We believe that the fuzzy modeling approach demonstrated here may supply a suitable framework for biomimicry, that is, the design of artificial systems based on mimicking a natural behavior observed in nature.