Uncertain rule-based fuzzy logic systems : introduction and new directions
著者
書誌事項
Uncertain rule-based fuzzy logic systems : introduction and new directions
Prentice Hall PTR, c2001
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注記
Includes bibliographical references (p. 530-546) and index
"This book presents an expanded and richer FL" -- on cover
内容説明・目次
内容説明
For courses in Neural Networks and Fuzzy Systems; Fuzzy Systems/Control; Fuzzy Logic.
The first book of its kind, this text explains how all kinds of uncertainties can be handled within the framework of a common theory and set of design tools-fuzzy logic systems-by moving the original fuzzy logic to the next level-type-2 fuzzy logic. It presents a complete development of both type-1 and type-2 fuzzy logic systems, showing how the expanded and richer fuzzy logic contains the original fuzzy logic within it. The text demonstrates, beyond a reasonable doubt, that when uncertainties are present in a problem, much better performance is obtained by using a type-2 fuzzy logic system than by using a type-1 fuzzy logic system.
目次
(NOTE: Each chapter concludes with Exercises.)I: PRELIMINARIES.
1. Introduction.
Rule-Based FLSs. A New Direction for FLSs. New Concepts and Their Historical Background. Fundamental Design Requirement. The Flow of Uncertainties. Existing Literature on Type-2 Fuzzy Sets. Coverage. Applicability Outside of Rule-Based FLSs. Computation.
Supplementary Material: Short Primers on Fuzzy Sets and Fuzzy Logic.
Primer on Fuzzy Sets. Primer on FL. Remarks.
2. Sources of Uncertainty.
Uncertainties in a FLS. Words Mean Different Things to Different People.
3. Membership Functions and Uncertainty.
Introduction. Type-1 Membership Functions. Type-2 Membership Functions. Returning to Linguistic Labels. Multivariable Membership Functions. Computation.
4. Case Studies.
Introduction. Forecasting of Time-Series. Knowledge Mining Using Surveys.
II: TYPE-1 FUZZY LOGIC SYSTEMS.
5. Singleton Type-1 Fuzzy Logic Systems: No Uncertainties.
Introduction. Rules. Fuzzy Inference Engine. Fuzzification and Its Effect on Inference. Defuzzification. Possibilities. Fuzzy Basis Functions. FLSs Are Universal Approximators. Designing FLSs. Case Study: Forecasting of Time-Series. Case Study: Knowledge Mining Using Surveys. A Final Remark. Computation.
6. Non-Singleton Type-1 Fuzzy Logic Systems.
Introduction. Fuzzification and Its Effect on Inference. Possibilities. FBFs. Non-Singleton FLSs Are Universal Approximators. Designing Non-Singleton FLSs. Case Study: Forecasting of Time-Series. A Final Remark. Computation.
III: TYPE-2 FUZZY SETS.
7. Operations on and Properties of Type-2 Fuzzy Sets.
Introduction. Extension Principle. Operations on General Type-2 Fuzzy Sets. Operations on Interval Type-2 Fuzzy Sets. Summary of Operations. Properties of Type-2 Fuzzy Sets. Computation.
8. Type-2 Relations and Compositions.
Introduction. Relations in General. Relations and Compositions on the Same Product Space. Relations and Compositions on Different Product Spaces. Composition of a Set with a Relation. Cartesian Product of Fuzzy Sets. Implications.
9. Centroid of a Type-2 Fuzzy Set: Type-Reduction.
Introduction. General Results for the Centroid. Generalized Centroid for Interval Type-2 Fuzzy Sets. Centroid of an Interval Type-2 Fuzzy Set. Type-Reduction: General Results. Type-Reduction: Interval Sets. Concluding Remark. Computation.
IV: TYPE-2 FUZZY LOGIC SYSTEMS.
10. Singleton Type-2 Fuzzy Logic Systems.
Introduction. Rules. Fuzzy Inference Engine. Fuzzification and Its Effect on Inference. Type-Reduction. Defuzzification. Possibilities. FBFs: The Lack Thereof. Interval Type-2 FLSs. Designing Interval Singleton Type-2 FLSs. Case Study: Forecasting of Time-Series. Case Study: Knowledge Mining Using Surveys. Computation.
11. Type-1 Non-Singleton Type-2 Fuzzy Logic Systems.
Introduction. Fuzzification and Its Effect on Inference. Interval Type-1 Non-Singleton Type-2 FLSs. Designing Interval Type-1 Non-Singleton Type-2 FLSs. Case Study: Forecasting of Time-Series. Final Remark. Computation.
12. Type-2 Non-Singleton Type-2 Fuzzy Logic Systems.
Introduction. Fuzzification and Its Effect on Inference. Interval Type-2 Non-Singleton Type-2 FLSs. Designing Interval Type-2 Non-Singleton Type-2 FLSs. Case Study: Forecasting of Time-Series. Computation.
13. TSK Fuzzy Logic Systems.
Introduction. Type-1 TSK FLSs. Type-2 TSK FLSs. Example: Forecasting of Compressed Video Traffic. Final Remark. Computation.
14. Epilogue.
Introduction. Type-2 Versus Type-1 FLSs. Appropriate Applications for a Type-2 FLS. Rule-Based Classification of Video Traffic. Equalization of Time-Varying Non-linear Digital Communication Channels. Overcoming CCI and ISI for Digital Communication Channels. Connection Admission Control for ATM Networks. Potential Application Areas for a Type-2 FLS.
A. Join, Meet, and Negation Operations For Non-Interval Type-2 Fuzzy Sets.
Introduction. Join Under Minimum or Product t-Norms. Meet Under Minimum t-Norm. Meet Under Product t-Norm. Negation. Computation.
B. Properties of Type-1 and Type-2 Fuzzy Sets.
Introduction. Type-1 Fuzzy Sets. Type-2 Fuzzy Sets.
C. Computation.
Type-1 FLSs. General Type-2 FLSs. Interval Type-2 FLSs.
References.
Index.
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