Abstract
Fuzzy graph theory is a fuzzy set generalization of classical graph theory suitable for preliminary analysis of many ecological systems. Fuzzy graph theory is applicable to the analysis of any dynamical system where the values of all state variables are known at at least two points in time. This paper presents some methods and algorithms of fuzzy graph theory, and uses fuzzy graph theory in an analysis of the compositional dynamics of an oak woods in Wisconsin, U.S.A. Three fuzzy relations for succession are compared using the same data to determine how the depiction of forest dynamics depends upon the characteristics of the chosen relation. The inherent minimum requirements for recognizing succession vary with each relation, and the relations from a hierarchy of rigor in requirements. The fuzzy graphs show that the observed successional trends are dependent upon the characteristics of each relation. Fuzzy graph theory is then used to analyze the time-variance of the system dynamics by comparing fuzzy graphs of succession for four consecutive time periods. The analysis shows only small changes in the system dynamics with time, demonstrating that the system is not strongly time-varying. The rate of system change, however, appears to be slowing. Finally, fuzzy graph theory is compared to vector field methods of dynamical system analysis.
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