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...

1. 1 Introduction The objective of this book is to introduce Monte Carlo methods to ?nd good approximate solutions to fuzzy optimization problems. Many crisp (nonfuzzy) optimization problems have algorithms to determine solutions. This is not true for fuzzy optimization. There are other things to discuss in fuzzy optimization, which we will do later onin the book, like? and

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...