Uncertain Rule-Based Fuzzy Logic Systems

• Type-2 fuzzy logic: Breakthrough techniques for modeling uncertainty
• Key applications: digital mobile communications, computer networking, and video traffic classification
• Detailed case studies: Forecasting time series and knowledge mining
• Contains 90+ worked examples, 110+ figures, and brief introductory primers on fuzzy logic and fuzzy sets
• Breakthrough fuzzy logic techniques for handling real-world uncertainty.

The world is full of uncertainty that classical fuzzy logic can't model. Now, however, there's an approach to fuzzy logic that can model uncertainty: "type-2" fuzzy logic. In this book, the developer of type-2 fuzzy logic demonstrates how it overcomes the limitations of classical fuzzy logic, enabling a wide range of applications from digital mobile communications to knowledge mining. Dr. Jerry Mendel presents a bottom-up approach that begins by introducing traditional "type-1" fuzzy logic, explains how it can be modified to handle uncertainty, and, finally, adds layers of complexity to handle increasingly sophisticated applications. Coverage includes:

• The sources of uncertainty and the role of membership functions
• Type-2 fuzzy sets: operations, properties, and centroids
• Singleton, non-singleton, and TSK Type 2 fuzzy logic systems
• Comparing "type-2" and "type 1" results
• Extensive applications coverage: digital mobile communications, computer networking, and video traffic classification

Two start-to-finish case studies: Forecasting time series and knowledge mining Carefully balanced between theory and design,the book contains over 90 worked examples and more than 110 figures. It is ideal for engineers, scientists, computer science researchers, and mathematicians interested in AI, rule-based systems, and modeling uncertainty. Since it contains brief introductory primers on fuzzy logic and fuzzy sets, it's accessible to virtually anyone with an undergraduate B.S. degree-including computing professionals designing and implementing rule-based systems.

Contents

I Preliminaries

1 Introduction

2 Sources of Uncertainty

3 Membership Functions and Uncertainty

4 Case Studies

II Type-1 Fuzzy Logic Systems

5 Singleton Type-1 Fuzzy Logic Systems: No Uncertainties

6 Non-singleton Type-1 Fuzzy Logic Systems

III Type-2 Fuzzy Sets

7 Operations on and Properties of Type-2 Fuzzy Sets

8 Type-2 Relations and Compositions

9 Centroid of a Type-2 Fuzzy Set: Type Reduction

IV Type-2 Fuzzy Logic Systems

10 Singleton Type-2 Fuzzy Logic Systems

11 Type-1-Non-singleton Type-2 Fuzzy Logic Systems

12 Type-2-Non-singleton Type-2 Fuzzy Logic Systems

13 TSK Fuzzy Logic Systems

14 Epilogue

Appendix A  Join, Meet and Negation Operations for Non- interval Type-2 Fuzzy Sets

Appendix B  Properties of Type-1 and Type-12 Fuzzy Sets

Appendix C  Computation

References