Reflecting the tremendous advances thathave taken place in the study of fuzzy set theory &fuzzy logic from 1988 to the present. This book notonly details the theoretical in these areas, butconsiders a broad variety of applications of fuzzysets and fuzzy logics as well. This text includingvarious methods for constructing membership functionsof fuzzy sets; the use of fuzzy logic for approximatereasoning in expert systems; fuzzy systems &controllers; fuzzy databases; fuzzy decision making,and engineering applications.
目 錄
Foreword.
Preface.
I. THEORY.
1. From Classical (Crisp) Sets to Fuzzy Sets: A Grand
Paradigm Shift.
Introduction. Crisp Sets: An Overview. Fuzzy Sets: Basic
Types. Fuzzy Sets: Basic Concepts. Characteristics and
Significance of the Paradigm Shift. Notes. Exercises.
2. Fuzzy Sets versus Crisp Sets.
Additional Properties of -Cuts. Representations of Fuzzy
Sets. Extension Principle for Fuzzy Sets. Notes. Exercises.
3. Operations on Fuzzy Sets.
Types of Operations. Fuzzy Complements. Fuzzy Intersections:
t- Norms. Fuzzy Unions: t-Conorms. Combinations of
Operations. Aggregation Operations. Notes. Exercises.
4. Fuzzy Arithmetic.
Fuzzy Numbers. Linguistic Variables. Arithmetic Operations
on Intervals. Arithmetic Operations on Fuzzy Numbers.
Lattice of Fuzzy Numbers. Fuzzy Equations. Notes. Exercises.
5. Fuzzy Relations.
Crisp versus Fuzzy Relations. Projections and Cylindric
Extensions. Binary Fuzzy Relations. Binary Relations on a
Single Set. Fuzzy Equivalence Relations. Fuzzy Compatibility
Relations. Fuzzy Ordering Relations. Fuzzy Morphisms. Sup-i
Compositions of Fuzzy Relations. Inf- Compositions of Fuzzy
Relations. Notes. Exercises.
6. Fuzzy Relation Equations.
General Discussion. Problem Partitioning. Solution Method.
Fuzzy Relation Equations Based on Sup-i Compositions. Fuzzy
Relation Equations Based on Inf-Compositions. Approximate
Solutions. The Use of Neural Networks. Notes. Exercises.
7. Possibility Theory.
Fuzzy Measures. Evidence Theory. Possibility Theory. Fuzzy
Sets and Possibility Theory. Possibility Theory versus
Probability Theory. Notes. Exercises.
8. Fuzzy Logic.
Classical Logic: An Overview. Multivalued Logics. Fuzzy
Propositions. Fuzzy Quantifiers. Linguistic Hedges.
Inference from Conditional Fuzzy Propositions. Inference
from Conditional and Qualified Propositions. Inference from
Quantified Propositions. Notes. Exercises.
9. Uncertainty-Based Information.
Information and Uncertainty. Nonspecificity of Crisp Sets.
Nonspecificity of Fuzzy Sets. Fuzziness of Fuzzy Sets.
Uncertainty in Evidence Theory. Summary of Uncertainty
Measures. Principles of Uncertainty. Notes. Exercises.
II. APPLICATIONS.
10. Constructing Fuzzy Sets and Operations on Fuzzy Sets.
General Discussion. Methods of Construction: An Overview.
Direct Methods with One Expert. Direct Methods with Multiple
Experts. Indirect Methods with One Expert. Indirect Methods
with Multiple Experts. Constructions from Sample Data.
Notes. Exercises.
11. Approximate Reasoning.
Fuzzy Expert Systems: An Overview. Fuzzy Implications.
Selection of Fuzzy Implications. Multiconditional
Approximate Reasoning. The Role of Fuzzy Relation
Equations. Interval-Valued Approximate Reasoning. Notes.
Exercises.
12. Fuzzy Systems.
General Discussion. Fuzzy Controllers: An Overview. Fuzzy
Controllers: An Example. Fuzzy Systems and Neural Networks.
Fuzzy Neural Networks. Fuzzy Automata. Fuzzy Dynamic
Systems. Notes. Exercises.
17. Miscellaneous Applications.
Introduction. Medicine. Economics. Fuzzy Systems and
Genetic Algorithms. Fuzzy Regression. Interpersonal
Communication. Other Applications. Notes. Exercises.
Appendix A. Neural Networks: An Overview.
Appendix B. Genetic Algorithms: An Overview.
Appendix C. Rough Sets versus Fuzzy Sets.
Appendix D. Proofs of Some Mathematical Theorems.
Appendix E. Glossary of Key Concepts.
Appendix F. Glossary of Symbols.
Bibliography.
Bibliographical Index.
Name Index.
Subject Index.
