Simulating Continuous Fuzzy Systems

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This book is the companion text to Simulating Fuzzy Systems which investigated discrete fuzzy systems through crisp discrete simulation. The current book studies continuous fuzzy dynamical systems using crisp continuous simulation. We start with a crisp continuous dynamical system whose evolution depends on a system of ordinary differential equations (ODEs). The system of ODEs contains parameters many of which have uncertain values. Usually point estimators for these uncertain parameters are used, but the resulting system will not display any uncertainty associated with these estimators. Instead we employ fuzzy number estimators, constructed from expert opinion or from data, for the uncertain parameters. Fuzzy number estimators produces a system of fuzzy ODEs to solve whose solution will be fuzzy trajectories for the variables. We use crisp continuous simulation to estimate the trajectories of the support and core of these fuzzy numbers in a variety of twenty applications of fuzzy dynamical systems. The applications range from Bungee jumping to the AIDS epidemic to dynamical models in economics.