Simulating Continuous Fuzzy Systems

Professor James J. Buckley, Leonard J. Jowers (auth.)9783540284550, 3-540-28455-9

This monograph studies continuous fuzzy dynamical systems using crisp continuous simulation. A crisp continuous dynamical system is presented 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 fuzzy number estimators are employed, constructed from expert opinion or from data, for the uncertain parameters. Fuzzy number estimators produce a system of fuzzy ODEs to solve whose solution will be fuzzy trajectories for the variables. The authors 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. This book is the companion text to “Simulating Fuzzy Systems” (Springer 2005) which investigated discrete fuzzy systems through crisp discrete simulation.

Table of contents :
Introduction….Pages 1-8
Fuzzy Sets….Pages 9-19
Fuzzy Estimation….Pages 21-32
Fuzzy Systems….Pages 33-37
Continuous Simulation Software….Pages 39-41
Simulation Optimization….Pages 43-47
Predator/Prey Models….Pages 49-53
An Arm’s Race Model….Pages 55-61
Bungee Jumping….Pages 63-67
Spread of Infectious Disease Model….Pages 69-74
Planetary Motion….Pages 75-79
Human Cannon Ball….Pages 81-86
Electrical Circuits….Pages 87-93
Hawks, Doves and Law-Abiders….Pages 95-104
Suspension System….Pages 105-110
Chemical Reactions….Pages 111-116
The AIDS Epidemic….Pages 117-124
The Machine/Service Queuing Model….Pages 125-131
A Self-Service Queuing Model….Pages 133-137
Symbiosis….Pages 139-143
Supply and Demand….Pages 145-149
Drug Concentrations….Pages 151-156
Three Species Competition….Pages 157-161
Flying a Glider….Pages 163-166
The National Economy….Pages 167-174
Sex Structured Population Models….Pages 175-179
Summary and Future Research….Pages 181-184
Matlab/Simulink Commands for Graphs….Pages 185-190