Uncertain Rule-Based Fuzzy Logic Systems
Introduction and New Directions
Published on 12. April 2001
Book
Hardback
576 pages
978-0-13-040969-0 (ISBN)
Description
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.
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.
More details
Language
English
Place of publication
Upper Saddle River
United States
Publishing group
Pearson Education (US)
Target group
College/higher education
Dimensions
Height: 187 mm
Width: 241 mm
Thickness: 25 mm
Weight
862 gr
ISBN-13
978-0-13-040969-0 (9780130409690)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
DR. JERRY MENDEL is Professor of Electrical Engineering and Associate Director of the Integrated Media Systems Center at the University of Southern California. He has published over 380 technical papers and seven books, and has been involved in fuzzy logic research for over 14 years.
Content
(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.
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.