Simulating Continuous Fuzzy Systems

1. Front Matter

   Pages I-XI

   PDF

2. Introduction

   Pages 1-8

3. Fuzzy Sets

   Pages 9-19

4. Fuzzy Estimation

   Pages 21-32

5. Fuzzy Systems

   Pages 33-37

6. Continuous Simulation Software

   Pages 39-41

7. Simulation Optimization

   Pages 43-47

8. Predator/Prey Models

   Pages 49-53

9. An Arm’s Race Model

   Pages 55-61

10. Bungee Jumping

    Pages 63-67

11. Spread of Infectious Disease Model

    Pages 69-74

12. Planetary Motion

    Pages 75-79

13. Human Cannon Ball

    Pages 81-86

14. Electrical Circuits

    Pages 87-93

15. Hawks, Doves and Law-Abiders

    Pages 95-104

16. Suspension System

    Pages 105-110

17. Chemical Reactions

    Pages 111-116

18. The AIDS Epidemic

    Pages 117-124

19. The Machine/Service Queuing Model

    Pages 125-131

20. A Self-Service Queuing Model

    Pages 133-137

1. 1 Introduction This book is written in two major parts. The ?rst part includes the int- ductory chapters consisting of Chapters 1 through 6. In part two, Chapters 7-26, we present the applications. This book continues our research into simulating fuzzy systems. We started with investigating simulating discrete event fuzzy systems ([7],[13],[14]). These systems can usually be described as queuing networks. Items (transactions) arrive at various points in the s- tem and go into a queue waiting for service. The service stations, preceded by a queue, are connected forming a network of queues and service, until the transaction ?nally exits the system. Examples considered included - chine shops, emergency rooms, project networks, bus routes, etc. Analysis of all of these systems depends on parameters like arrival rates and service rates. These parameters are usually estimated from historical data. These estimators are generally point estimators. The point estimators are put into the model to compute system descriptors like mean time an item spends in the system, or the expected number of transactions leaving the system per unit time. We argued that these point estimators contain uncertainty not shown in the calculations. Our estimators of these parameters become fuzzy numbers, constructed by placing a set of con?dence intervals one on top of another. Using fuzzy number parameters in the model makes it into a fuzzy system. The system descriptors we want (time in system, number leaving per unit time) will be fuzzy numbers.

• Fuzzy
• Fuzzy System Theory
• Genetic Algorithms
• MATLAB
• Simulation
• Simulation of Fuzzy Systems
• System
• differential equation
• dynamische Systeme
• fuzzy set
• fuzzy system
• model
• optimization
• uncertainty

• Department of Mathematics, University of Alabama at Birmingham, Birmingham, USA

  James J. Buckley

• Department of Computer and Information Sciences, University of Alabama at Birmingham, Birmingham, USA

  Leonard J. Jowers

Policies and ethics