Uncertain Rule-Based Fuzzy Logic Systems : Introduction and New Directions / Edition 1

Uncertain Rule-Based Fuzzy Logic Systems : Introduction and New Directions / Edition 1

by Jerry M. Mendel
     
 

  • 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

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Overview

  • 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.

SOFTWARE RESOURCES

Online software includes more than 30 companion MATLAB m-files for implementing a wide variety of type-1 and type-2 fuzzy logic systems.

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Product Details

ISBN-13:
9780130409690
Publisher:
Prentice Hall
Publication date:
12/29/2000
Edition description:
New Edition
Pages:
560
Product dimensions:
6.80(w) x 9.00(h) x 1.20(d)

Table of Contents

(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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