Fuzzy Systems Design Principles is a valuable guide and reference for practitioners looking to employ fuzzy logic concepts in the design and deployment of actual fuzzy systems. This book concentrates on the basic If–Then fuzzy algorithm, one of the most popular algorithms implemented today. The If–Then structure is applicable not only to many types of problems such as control, classification, modeling, pattern recognition, and diagnostics, but is also comprised of building blocks used in the development of fuzzy systems used in today s electronic and software products. Brimming with tips and insights into the design process, Fuzzy Systems Design Principles presents a balanced mixture of theory and application within a typical design framework. Readers will learn to make informed choices when selecting design options and to verify chosen principles with commonsense reasoning. The design principles are presented as "things to consider" rather than as "things to do." In this way, the reader′s creativity is not restricted, and one universal philosophy, which does not exist, is not claimed. Topics covered focus on the identification and resolution of the practical design issues which are often considered "beyond the scope" in much of the current literature. These discussions originate from a set of linguistic design criteria that define the objective patterns frequently used by the designers. In light of the linguistic design criteria, readers will be able to employ heuristic solutions in a systematic manner by using the suggested mathematical representations.
Chapter 1: Introduction.
1.1 Partial Truth and Fuzziness.
1.2 Foundation of Fuzzy Systems.
1.3 Fuzzy Systems at Work.
1.4 Fuzzy System Design.
1.5 How to Use This Book Effectively.
1.6 Terminology and Conventions.
Chapter 2: Theory.
2.1 Crisp Versus Fuzzy Sets.
2.2 From Fuzzy Sets to Fuzzy Events.
2.3 Fuzzy Logic and Linguistics.
2.4 Practical Fuzzy Measures.
2.5 Fuzzy Set Operations.
2.6 Properties of Fuzzy Sets.
2.7 Fuzzification Techniques.
2.8 Alpha Cuts.
2.9 Relational Inference.
2.10 Compositional Inference.
2.11 Linguistic Variables and Logic Operators.
2.12 Inference Using Fuzzy Variables.
2.13 Fuzzy Implication.
2.14 Fuzzy Systems and Algorithms.
2.16 Adaptive Fuzzy Systems and Algorithms.
2.17 Expert Systems Versus Fuzzy Inference Engines.
Chapter 3: The Basic Fuzzy Inference Algorithm.
3.2 Overall Algorithm.
3.3 Input Data Processing.
3.4 Evaluating Antecedent Fuzzy Variables.
3.5 Left–Hand–Side Computations.
3.6 Right–Hand–Side Computations.
3.7 Output Processing.
Chapter 4: Conceptual Design.
4.2 Fuzzy System Design and Its Elements.
4.3 Design Options, Processes, and Background.
4.5 Knowledge Acquisition.
4.6 The First Principle of Fuzzy Inference Design.
4.7 Linguistic Design Criteria.
4.8 Application of the Design Criteria.
4.9 Systems Ontology and Problem Types.
4.10 Useful Tools Supporting Design.
Recommended Books for Design.
Chapter 5: Fuzzy Variable Design.
5.1 Introduction to Fuzzy Variable Design.
5.2 Data–Driven Fuzzy Variable Design.
5.3 Linguistic Fuzzy Variable Design.
5.4 Practical Design Considerations.
Chapter 6: Membership Function Shape Analysis.
6.1 Introduction to Shape Analysis.
6.2 Membership Function Height.
6.3 Membership Function Line Style.
Chapter 7: Composing Fuzzy Rules.
7.2 Basic Logic Operators.
7.3 Logic Operator Design Issues.
7.4 Rule Formation Per Inference Type.
7.5 Rule Composition Strategies.
7.6 Paradoxical Cases.
7.7 Membership Function Shape Effects.
Chapter 8: Implication Design.
8.2 Selecting Implication Operators.
8.3 Behavioral Properties.
8.4 Aggregation Design.
8.5 Designing a Defuzzification/Decomposition Process.
8.6 Interpreting Output Fuzzy Sets.
Appendix: The Basic Fuzzy Inference Algorithm.
Dr. Sheldon L. Trubatch is currently a partner at the law firm of Winston & Strawn, where he specializes in nuclear and administrative law. He is also developing applications of fuzzy logic to support legal and regulatory decision making. Previously, Dr. Trubatch was a physics professor at California State University, Long Beach. Among his research areas was the application of mathematical techniques to the description of biological systems. Dr. Trubatch has a J.D. from Columbia University School of Law and a Ph.D. in physics from Brandeis University.