An application of fuzzy set theory for seral-class constraints in forest planning models

Timber harvesting is often regulated by seral stage constraints that limit the amount of area available for harvest, and, concomitantly, the state of the residual forest. Typically, crisp seral-class boundaries are used in forest planning, but they fail to recognize that stands develop slowly into and out of seral classes, and that stands near a seral-class boundary have characteristics of adjacent seral classes. This can cause difficulties for managers when abrupt changes in the amount of a seral class occur as stands pass through a crisp seral boundary. As an alternative, we defined seral stages using fuzzy set theory that assigns stands partial membership in seral stages, thus providing a mechanism for incorporating natural stand dynamics within seral classes. We then simulated a series of scenarios with a harvest scheduling model that was constrained by the crisp and fuzzy set seral definitions and compared harvest levels and the amount of seral classes present over a 250-year planning horizon. The fuzzy seral definition better mimicked stand development and produced a smoother accumulation of older seral stands, resulting in a higher and more uniform level of harvest.