Mathematical modeling of observed natural behavior: a fuzzy logic approach

Fuzzy modeling is routinely used to transform the knowledge of an expert, be it a physician or a process operator, into a mathematical model. The emphasis is on constructing a fuzzy expert system that replaces the human expert. In this paper, we advocate a different application of fuzzy modeling, namely, as a tool that can assist human observers in the difficult task of transforming their observations into a mathematical model. In many fields of science, including biology, psychology and economy, human observers have provided linguistic descriptions and explanations of various systems. However, to study these phenomena in a systematic manner, there is a need to construct a suitable mathematical model, a process that usually requires subtle mathematical understanding. Fuzzy modeling is a simple, direct, and natural approach for transforming the linguistic description into a mathematical model. Furthermore, fuzzy modeling offers a unique advantage—the close relationship between the linguistic description and the mathematical model can be used to verify the validity of the verbal explanation suggested by the observer. We demonstrate this using an example of territorial behavior of fish.