- 原书名：Fuzzy Set Theory and its Applications
- 原出版社： Springer
List of Figures
List of Tables
Preface to the Fourth Edition
1 Introduction to Fuzzy Sets
1.1 Crispness, Vagueness, Fuzziness, Uncertainty
1.2 Fuzzy Set Theory
Part I: Fuzzy Mathematics
2 Fuzzy Sets--Basic Definitions
2.1 Basic Definitions
2.2 Basic Set-Theoretic Operations for Fuzzy Sets
3.1 Types of Fuzzy Sets
3.2 Further Operations on Fuzzy Sets
3.2.1 Algebraic Operations
3.2.2 Set-Theoretic Operations
3.2.3 Criteria for Selecting Appropriate Aggregation Operators
4 Fuzzy Measures and Measures of Fuzziness
The primary goal of this book is to help to close this gap--to provide a textbook for courses in fuzzy set theory and a book that can be used as an introduction.
One of the areas in which fuzzy sets have been applied most extensively is in modeling for managerial decision making. Therefore, this area has been selected for more detailed consideration. The information has been divided into two volumes. The first volume contains the basic theory of fuzzy sets and some areas of application. It is intended to provide extensive coverage of the theoretical and applicational approaches to fuzzy sets. Sophisticated formalisms have not been included. I have tried to present the basic theory and its extensions in enough detail to be comprehended by those who have not been exposed to fuzzy set theory. Examples and exercises serve to illustrate the concepts even more clearly. For the interested or more advanced reader, numerous references to recent literature are included that should facilitate studies of specific areas in more detail and on a more advanced level.
The second volume is dedicated to the application of fuzzy set theory to the area of human decision making. It is self-contained in the sense that all concepts used are properly introduced and defined. Obviously this cannot be done in the same breadth as in the first volume. Also the coverage of fuzzy concepts in the second volume is restricted to those that are directly used in the models of decision making.
It is advantageous but not absolutely necessary to go through the first volume before studying the second. The material in both volumes has served as texts in teaching classes in fuzzy set theory and decision making in the United States and in Germany. Each time the material was used, refinements were made, but the author welcomes suggestions for further improvements.
The target groups were students in business administration, management science, operations research, engineering, and computer science. Even though no specific mathematical background is necessary to understand the books, it is assumed that the students have some background in calculus, set theory, operations research, and decision theory.
I would like to acknowledge the help and encouragement of all the students, particularly those at the Naval Postgraduate School in Monterey and at the Institute of Technology in Aachen (F.R.G.), who improved the manuscripts before they became textbooks. I also thank Mr. Hintz, who helped to modify the different versions of the book, worked out the examples, and helped to make the text as understandable as possible. Ms. Grefen typed the manuscript several times without losing her patience. I am also indebted to Kluwer Academic Publishers for making the publication of this book possible.
In the two decades since its inception, the theory has matured into a wideranging collection of concepts and techniques for dealing with complex phenomena that do not lend themselves to analysis by classical methods based on probability theory and bivalent logic. Nevertheless, a question that is frequently raised by the skeptics is: Are there, in fact, any significant problem-areas in which the use of the theory of fuzzy sets leads to results that could not be obtained by classical methods?
Professor Zimmermann's treatise provides an affirmative answer to this question. His comprehensive exposition of both the theory and its applications explains in clear terms the basic concepts that underlie the theory and how they relate to their classical counterparts. He shows through a wealth of examples the ways in which the theory can be applied to the solution of realistic problems, particularly in the realm of decision analysis, and motivates the theory by applications in which fuzzy sets play an essential role.
An important issue in the theory of fuzzy sets that does not have a counterpart in the theory of crisp sets relates to the combination of fuzzy sets through disjunction and conjunction or, equivalently, union and intersection. Professor Zimmermann and his associates at the Technical University of Aachen have made many important contributions to this problem and were the first to introduce the concept of a parametric family of connectives that can be chosen to fit a particular application. In recent years, this issue has given rise to an extensive literature dealing with t-norms and related concepts that link some aspects of the theory of fuzzy sets to the theory of probabilistic metric spaces developed by Karl Menger.
Another important issue addressed in Professor Zimmermann's treatise relates to the distinction between the concepts of probability and possibility, with the latter concept having a close connection with that of membership in a fuzzy set. The concept of possibility plays a particularly important role in the representation of meaning, in the management of uncertainty in expert systems, and in applications of the theory of fuzzy sets to decision analysis.
As one of the leading contributors to and practitioners of the use of fuzzy sets in decision analysis, Professor Zimmermann is uniquely qualified to address the complex issues arising in fuzzy optimization problems and, especially, fuzzy mathematical programming and multicriterion decision making in a fuzzy environment. His treatment of these topics is comprehensive, up-to-date, and illuminating.
In sum, Professor Zimmermann's treatise is a major contribution to the literature of fuzzy sets and decision analysis. It presents many original results and incisive analyses. And, most importantly, it succeeds in providing an excellent introduction to the theory of fuzzy sets--an introduction that makes it possible for an uninitiated reader to obtain a clear view of the theory and learn about its applications in a wide variety of fields.
The writing of this book was a difficult undertaking. Professor Zimmermann deserves to be congratulated on his outstanding accomplishment and thanked for contributing so much over the past decade to the advancement of the theory of fuzzy sets as a scientist, educator, administrator, and organizer.