 # Fuzzy Sets and Fuzzy Logic: Theory and Applications, 1st edition

• Bo Yuan
• George J. Klir

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## Overview

Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic from 1988 to the present, this book not only details the theoretical advances in these areas, but considers a broad variety of applications of fuzzy sets and fuzzy logic as well. KEY TOPICS: Theoretical aspects of fuzzy set theory and fuzzy logic are covered in Part I of the text, including: basic types of fuzzy sets; connections between fuzzy sets and crisp sets; the various aggregation operations of fuzzy sets; fuzzy numbers and arithmetic operations on fuzzy numbers; fuzzy relations and the study of fuzzy relation equations. Part II is devoted to applications of fuzzy set theory and fuzzy logic, including: various methods for constructing membership functions of fuzzy sets; the use of fuzzy logic for approximate reasoning in expert systems; fuzzy systems and controllers; fuzzy databases; fuzzy decision making; and engineering applications. MARKET: For everyone interested in an introduction to fuzzy set theory and fuzzy logic.

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.

13. Pattern Recognition.

Introduction. Fuzzy Clustering. Fuzzy Pattern Recognition. Fuzzy Image Processing. Notes. Exercises.

14. Fuzzy Databases and Information Retrieval Systems.

General Discussion. Fuzzy Databases. Fuzzy Information Retrieval. Notes. Exercises.

15. Fuzzy Decision Making.

General Discussion. Individual Decision Making. Multiperson Decision Making. Multicriteria Decision Making. Multistage Decision Making. Fuzzy Ranking Methods. Fuzzy Linear Programming. Notes. Exercises.

16. Engineering Applications.

Introduction. Civil Engineering. Mechanical Engineering. Industrial Engineering. Computer Engineering. Reliability Theory. Robotics. 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.