SIMULATING CONTINUOUS FUZZY SYSTEMS: I

In previous studies we first concentrated on utilizing crisp simulationto produce discrete event fuzzy systems simulations. Then we extendedthis research to the simulation of continuous fuzzy systems models. In this paperwe continue our study of continuous fuzzy systems using crisp continuoussimulation. Consider a crisp continuous system whose evolution depends ondifferential equations. Such a system contains a number of parameters thatmust be estimated. Usually point estimates are computed and used in themodel. However these point estimates typically have uncertainty associatedwith them. We propose to incorporate uncertainty by using fuzzy numbers asestimates of these unknown parameters. Fuzzy parameters convert the crispsystem into a fuzzy system. Trajectories describing the behavior of the systembecome fuzzy curves. We will employ crisp continuous simulation to estimatethese fuzzy trajectories. Three examples are discussed.

Keywords:

Fuzzy systems , Fuzzy differential equations , Simulation , Uncertainty