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 number
