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Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions, 2nd Edition 2nd ed. 2017 [Hardback]

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  • Formāts: Hardback, 684 pages, height x width: 235x155 mm, weight: 1546 g, 187 Tables, color; 192 Illustrations, color; 23 Illustrations, black and white; XXII, 684 p. 215 illus., 192 illus. in color., 1 Hardback
  • Izdošanas datums: 29-May-2017
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319513699
  • ISBN-13: 9783319513690
Citas grāmatas par šo tēmu:
Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions, 2nd Edition 2nd ed. 2017Palielināt
  • Formāts: Hardback, 684 pages, height x width: 235x155 mm, weight: 1546 g, 187 Tables, color; 192 Illustrations, color; 23 Illustrations, black and white; XXII, 684 p. 215 illus., 192 illus. in color., 1 Hardback
  • Izdošanas datums: 29-May-2017
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319513699
  • ISBN-13: 9783319513690
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783319513690.html
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The second edition of this textbook provides a fully updated approach to fuzzy sets and systems that can model uncertainty — ie “type-2” fuzzy sets and systems. The author demonstrates how to overcome the limitations of classical fuzzy sets and systems, enabling a wide range of applications from time-series forecasting to knowledge mining. In this new edition, a bottom-up approach is presented that begins by introducing classical (type-1) fuzzy sets and systems, and then explains how they can be modified to handle uncertainty. The author covers fuzzy-logic rule-based systems – from type-1 to interval type-2 to general type-2 – in one volume. For hands-on experience, the book provides information on using MatLab Software to complement the content and how m-files can be accessed. The book features a full suite of classroom material.

1 Introduction
1(24)
1.1 What This Book Is About
1(6)
1.2 The Structure of a Rule-Based Fuzzy System
7(2)
1.3 A New Direction for Fuzzy Systems
9(1)
1.4 Fundamental Design Requirement
10(1)
1.5 An Impressionistic Brief History of Type-1 Fuzzy Sets and Fuzzy Logic
10(1)
1.6 Literature on Type-2 Fuzzy Sets and Fuzzy Systems
11(4)
1.6.1 Early Literature: 1975--1992
12(1)
1.6.2 Publications that Heavily Influenced the First Edition of This Book
13(1)
1.6.3 Application Papers
14(1)
1.7 Coverage
15(4)
1.8 Applicability Outside of Rule-Based Fuzzy Systems
19(1)
1.9 Computation
19(6)
References
20(5)
2 Type-1 Fuzzy Sets and Fuzzy Logic
25(76)
2.1 Crisp Sets
25(1)
2.2 Type-1 Fuzzy Sets and Associated Concepts
26(11)
2.2.1 Lotfi A. Zadeh
27(1)
2.2.2 Type-1 Fuzzy Set Defined
28(4)
2.2.3 Type-1 Fuzzy Numbers
32(1)
2.2.4 Linguistic Variables
33(3)
2.2.5 Returning to Linguistic Labels from Numerical Values of MFs
36(1)
2.3 Set Theoretic Operations for Crisp Sets
37(1)
2.4 Set Theoretic Operations for Type-1 Fuzzy Sets
38(4)
2.5 Crisp Relations and Compositions on the Same Product Space
42(2)
2.6 Fuzzy Relations and Compositions on the Same Product Space
44(2)
2.7 Crisp Relations and Compositions on Different Product Spaces
46(3)
2.8 Fuzzy Relations and Compositions on Different Product Spaces
49(3)
2.9 Hedges
52(2)
2.10 Extension Principle
54(6)
2.11 a-Cuts
60(2)
2.12 Representing Type-1 Fuzzy Sets Using α-Cuts
62(4)
2.13 Functions of Type-1 Fuzzy Sets Computed by Using α-Cuts
66(3)
2.14 Multivariable MFs and Cartesian Products
69(1)
2.15 Crisp Logic
70(4)
2.16 From Crisp Logic to Fuzzy Logic
74(3)
2.17 Mamdani (Engineering) Implications
77(5)
2.18 Remarks
82(19)
Appendix 1 Properties of Type-1 Fuzzy Sets
84(2)
Exercises
86(10)
References
96(5)
3 Type-1 Fuzzy Systems
101(60)
3.1 Type-1 Fuzzy Systems
101(1)
3.2 Rules
101(5)
3.3 Fuzzifier
106(1)
3.4 Fuzzy Inference Engine
107(13)
3.4.1 General Results
107(3)
3.4.2 Type-1 Rule Partitions
110(4)
3.4.3 Fuzzification and Its Effects on Inference
114(6)
3.5 Combining Fired-Rule Output Sets on the Way to Defuzzification
120(3)
3.5.1 Mamdani Fuzzy System: Combining Using Set-Theoretic Operations
120(1)
3.5.2 Mamdani Fuzzy System Combining Using a Weighted Combination
121(2)
3.5.3 Mamdani and TSK Fuzzy Systems Combining During Defuzzification
123(1)
3.6 Defuzzifier
123(5)
3.6.1 Mamdani Fuzzy System: Centroid Defuzzifier
124(1)
3.6.2 Mamdani Fuzzy System: Height Defuzzifier
125(1)
3.6.3 Mamdani Fuzzy System: COS Defuzzifier
125(2)
3.6.4 TSK Fuzzy System Defuzzifiers
127(1)
3.7 Comprehensive Example
128(3)
3.8 Fuzzy Basis Functions
131(8)
3.9 Remarks and Insights
139(22)
3.9.1 Layered Architecture Interpretations of a Fuzzy System
139(2)
3.9.2 Universal Approximation by Fuzzy Systems
141(1)
3.9.3 Continuity of Fuzzy Systems
142(2)
3.9.4 Rule Explosion and Some Ways to Control It
144(2)
3.9.5 Rule Interpretability
146(2)
Exercises
148(6)
References
154(7)
4 Type-1 Fuzzy Systems: Design Methods and Applications
161(84)
4.1 Designing Type-1 Fuzzy Systems
161(9)
4.2 Some Design Methods
170(17)
4.2.1 One-Pass Methods
170(3)
4.2.2 Least Squares Method
173(3)
4.2.3 Derivative-Based Methods
176(3)
4.2.4 SVD-QR Method
179(2)
4.2.5 Derivative-Free Methods
181(5)
4.2.6 Iterative Design Methods
186(1)
4.2.7 Remarks
186(1)
4.3 Case Study: Forecasting of Time Series
187(12)
4.3.1 Mackey--Glass Chaotic Time Series
188(1)
4.3.2 One-Pass Design: Singleton Fuzzification
189(2)
4.3.3 Derivative-Based Design: Singleton Fuzzification
191(3)
4.3.4 A Change in the Measurements
194(1)
4.3.5 One-Pass Design: Non-singleton Fuzzification
195(2)
4.3.6 Derivative-Based Design: Non-singleton Fuzzification
197(2)
4.3.7 Final Remark
199(1)
4.4 Case Study: Knowledge Mining Using Surveys
199(15)
4.4.1 Methodology for Knowledge Mining
200(2)
4.4.2 Survey Results
202(1)
4.4.3 Determining Type-1 Fuzzy Sets from Survey Results
203(3)
4.4.4 What Does One Do with a Histogram of Responses?
206(1)
4.4.5 Averaging the Responses: Consensus FLAs
207(2)
4.4.6 Preserving All of the Responses
209(1)
4.4.7 On Multiple Indicators
210(1)
4.4.8 How to Use a FLA
210(2)
4.4.9 Connections to the Perceptual Computer
212(2)
4.5 Forecasting of Compressed Video Traffic Using Mamdani and TSK Fuzzy Systems
214(4)
4.5.1 Forecasting I Frame Sizes: General Information
215(1)
4.5.2 Forecasting I Frame Sizes: Using the Same Number of Rules
216(1)
4.5.3 Forecasting I Frame Sizes: Using the Same Number of Design Parameters
217(1)
4.6 Rule-Based Classification of Video Traffic
218(8)
4.6.1 Selected Features
220(1)
4.6.2 MFs for the Features
220(1)
4.6.3 Rules and Their Parameters
221(1)
4.6.4 Computational Formulas for the RBC
222(1)
4.6.5 Optimization of Rule Design Parameters
223(1)
4.6.6 Testing the FL RBC
224(1)
4.6.7 Results and Conclusions
225(1)
4.7 Case Study: Fuzzy Logic Control
226(19)
4.7.1 Early History of Fuzzy Control
226(1)
4.7.2 What Is a Type-1 Fuzzy Logic Controller (FLC)?
227(2)
4.7.3 Fuzzy PID Control
229(5)
Appendix 1 Proof of Theorem 4.1
234(2)
Exercises
236(3)
References
239(6)
5 Sources of Uncertainty
245(14)
5.1 Uncertainties in a Fuzzy System
245(5)
5.1.1 Uncertainty: General Discussions
245(1)
5.1.2 Uncertainties and Sets
246(1)
5.1.3 Uncertainties in a Fuzzy System
247(3)
5.2 Words Mean Different Things to Different People
250(9)
Exercises
256(1)
References
257(2)
6 Type-2 Fuzzy Sets
259(48)
6.1 The Concept of a Type-2 Fuzzy Set
259(3)
6.2 Definitions of a General Type-2 Fuzzy Set and Associated Concepts
262(11)
6.3 Definitions of an IT2 FS and Associated Concepts
273(6)
6.4 Examples of Two Popular FOUs
279(3)
6.5 Interval Type-2 Fuzzy Numbers
282(2)
6.6 Different Kinds of T2 FSs: Hierarchy
284(3)
6.7 Mathematical Representations for T2 FSs
287(10)
6.7.1 Vertical Slice Representation
287(2)
6.7.2 Wavy Slice Representation
289(1)
6.7.3 Horizontal Slice Representation
290(4)
6.7.4 Which Representations Are Most Useful for Optimal Design Applications?
294(3)
6.8 Representing Non T2 FSs as T2 FSs
297(1)
6.9 Returning to Linguistic Labels for T2 FSs
298(2)
6.10 Multivariate Membership Functions
300(7)
Exercises
301(3)
References
304(3)
7 Working with Type-2 Fuzzy Sets
307(78)
7.1 Introduction and Guide for the Reader
307(1)
7.2 Set-Theoretic Operations for GT2 FSs Computed Using the Extension Principle
308(17)
7.2.1 Union of GT2 FSs
309(5)
7.2.2 Intersection of GT2 FSs
314(6)
7.2.3 Complement of a GT2 FS
320(2)
7.2.4 Remarks
322(3)
7.3 Set-Theoretic Operations for IT2 FSs
325(6)
7.3.1 Union of IT2 FSs
326(2)
7.3.2 Intersection of IT2 FSs
328(1)
7.3.3 Complement of an IT2 FS
329(2)
7.4 Set-Theoretic Operations for GT2 FSs Computed by Using Horizontal Slices
331(10)
7.4.1 Union of GT2 FSs
332(4)
7.4.2 Intersection of GT2 FSs
336(4)
7.4.3 Complement of a GT2 FS
340(1)
7.4.4 Historical Remarks
340(1)
7.5 Observations About Set Theory Computations
341(1)
7.6 Relations in General
341(3)
7.7 Type-2 Relations and Compositions on the Same Product Space
344(3)
7.8 Type-2 Relations and Compositions on Different Product Spaces
347(1)
7.9 Compositions of a T2 FS with a Type-2 Relation
348(2)
7.10 Type-2 Hedges
350(1)
7.11 Extension Principle for T2 FSs
351(2)
7.11.1 Extension Principle for IT2 FSs
351(1)
7.11.2 Extension Principle for GT2 FSs
352(1)
7.12 Functions of GT2 FSs Computed Using a-Planes
353(1)
7.13 Cartesian Product of T2 FSs
353(1)
7.14 Implications
354(31)
Appendix 1 Properties of T2 FSs
355(7)
Appendix 2 Proofs
362(10)
Exercise
372(9)
References
381(4)
8 Type-Reduction
385(64)
8.1 Introduction
385(1)
8.2 Interval Weighted Average (IWA)
386(17)
8.2.1 Formulation of the IWA
386(2)
8.2.2 Computing the IWA
388(3)
8.2.3 KM Algorithms
391(5)
8.2.4 Enhanced KM Algorithms
396(3)
8.2.5 Enhanced Iterative Algorithm with Stopping Condition (EIASC)
399(4)
8.2.6 Remarks
403(1)
8.3 Type-Reduction for IT2 FSs and Fuzzy Systems
403(17)
8.3.1 Centroid Type-Reduction for IT2 Fuzzy Sets
404(7)
8.3.2 Centroid Type-Reduction in an IT2 Fuzzy System
411(1)
8.3.3 Height Type-Reduction in an IT2 Fuzzy System
412(2)
8.3.4 Center-of-Sets (COS) Type-Reduction in an IT2 Fuzzy System
414(2)
8.3.5 Type-Reduction Example
416(1)
8.3.6 Remarks and Insights
417(3)
8.4 Type-Reduction for GT2 FSs and Fuzzy Systems
420(29)
8.4.1 Centroid Type-Reduction for GT2 Fuzzy Sets
422(9)
8.4.2 Centroid Type-Reduction in a GT2 Fuzzy System
431(1)
8.4.3 COS Type-Reduction in a GT2 Fuzzy System
431(1)
Appendix 1 A Wavy-Slice Approach to Type-Reduction
431(3)
Appendix 2 Type-Reduction Properties
434(7)
Exercises
441(4)
References
445(4)
9 Interval Type-2 Fuzzy Systems
449(80)
9.1 Introduction
449(1)
9.2 Rules
450(2)
9.3 Fuzzifier
452(1)
9.4 Fuzzy Inference Engine
453(26)
9.4.1 General Results
454(4)
9.4.2 Fuzzification and Its Effects on Inference for IT2 Fuzzy Systems
458(21)
9.5 Combining Fired Rule Output Sets on the Way to Defuzzification
479(2)
9.5.1 Combining Using Set Theoretic Operations in an IT2 Mamdani Fuzzy System
479(2)
9.5.2 Combining During Defuzzification in an IT2 Mamdani Fuzzy System
481(1)
9.6 Type-Reduction + Defuzzification
481(8)
9.6.1 Centroid Type-Reduction + Defuzzification for an IT2 Mamdani Fuzzy System
481(1)
9.6.2 Height Type-Reduction + Defuzzification for an IT2 Mamdani Fuzzy System
482(1)
9.6.3 COS Type-Reduction + Defuzzification for an IT2 Mamdani Fuzzy System
483(1)
9.6.4 Type-Reduction + Defuzzification for an IT2 TSK Fuzzy System
484(4)
9.6.5 Novelty Partitions
488(1)
9.7 Comprehensive Example
489(5)
9.8 Approximate Type-Reduction + Defuzzification (Wu-Mendel Uncertainty Bounds) for IT2 Mamdani Fuzzy Systems
494(3)
9.9 Direct Defuzzification
497(3)
9.9.1 Nie--Tan (NT) Direct Defuzzification
498(2)
9.9.2 Biglarbegian--Melek--Mendel (BMM) Direct Defuzzification
500(1)
9.10 Summary
500(2)
9.11 Comprehensive Example Continued
502(2)
9.12 IT2 Fuzzy Basis Functions
504(3)
9.13 Remarks and Insights
507(22)
9.13.1 Layered Architecture Interpretations of an IT2 Fuzzy System
508(2)
9.13.2 Fundamental Differences Between T1 and IT2 Fuzzy Systems
510(1)
9.13.3 Universal Approximation by IT2 Fuzzy Systems
510(1)
9.13.4 Continuity of IT2 Fuzzy Systems
511(4)
9.13.5 Rule Explosion and Some Ways to Control It
515(1)
9.13.6 Rule Interpretability
516(1)
9.13.7 Historical Notes
516(3)
Exercises
519(5)
References
524(5)
10 Interval Type-2 Fuzzy Systems: Design Methods and Applications
529(88)
10.1 Designing IT2 Fuzzy Systems
529(8)
10.2 Some Design Methods
537(17)
10.2.1 IT2 WM Method
537(1)
10.2.2 Least-Squares Method
538(2)
10.2.3 Derivative-Based Methods
540(4)
10.2.4 SVD-QR Method
544(2)
10.2.5 Derivative-Free Methods
546(4)
10.2.6 Iterative Design Methods
550(1)
10.2.7 Remarks
551(3)
10.3 Case Study: Forecasting of Time-Series
554(13)
10.3.1 Forecasting of Time Series When the Measurement Noise Is Stationary
554(4)
10.3.2 Forecasting of Time Series When the Measurement Noise Is Nonstationary
558(9)
10.4 Case Study: Knowledge Mining Using Surveys
567(15)
10.4.1 Determining the IT2 FSs for the Vocabulary
567(2)
10.4.2 What Does One Do with a Histogram of Responses?
569(1)
10.4.3 IT2 Consensus FLAs
570(6)
10.4.4 Remark
576(1)
10.4.5 How to Use the IT2 FLA
577(2)
10.4.6 Connections to the Perceptual Computer
579(3)
10.5 Forecasting of Compressed Video Traffic Using IT2 Mamdani and TSK Fuzzy Systems
582(4)
10.5.1 Forecasting I Frame Sizes: Using the Same Number of Rules
583(2)
10.5.2 Forecasting I Frame Sizes: Using the Same Number of Design Parameters
585(1)
10.5.3 Conclusion
585(1)
10.6 IT2 Rule-Based Classification of Video Traffic
586(4)
10.6.1 FOUs for the Features
587(1)
10.6.2 Rules and Their Parameters
587(1)
10.6.3 Fuzzifiers
588(1)
10.6.4 Computational Formulas for the IT2 RBCs
588(1)
10.6.5 Optimization of the Rule Design Parameters
589(1)
10.6.6 Results and Conclusions
590(1)
10.7 Equalization of Time-Varying Nonlinear Digital Communication Channels
590(10)
10.7.1 Preliminaries for Channel Equalization
592(1)
10.7.2 Why an IT2 FAF Is Needed
593(3)
10.7.3 Designing the IT2 FAFs
596(1)
10.7.4 Simulations and Conclusions
597(3)
10.8 IT2 Fuzzy Logic Control
600(8)
10.8.1 What Is an IT2 Fuzzy Logic Controller (FLC)?
600(1)
10.8.2 IT2 Fuzzy PID Control
601(1)
10.8.3 Simulation Results (IT2-FPID Versus T1-FPID and PID)
602(6)
10.9 Other Applications
608(9)
Exercises
609(5)
References
614(3)
11 General Type-2 Fuzzy Systems
617(58)
11.1 Introduction
617(3)
11.2 Rules
620(2)
11.3 Fuzzifier
622(1)
11.4 Fuzzy Inference Engine
622(5)
11.5 Combining Fired Rule Output Sets on the Way to Defuzzification
627(2)
11.5.1 Combining Using Set Theoretic Operations in a WH GT2 Mamdani Fuzzy System
628(1)
11.5.2 Combining During Defuzzification in a WH GT2 Mamdani Fuzzy System
629(1)
11.6 Type-Reduction
629(5)
11.6.1 Centroid Type-Reduction for a WH GT2 Mamdani Fuzzy System
630(1)
11.6.2 Center-of Sets Type-Reduction for a WH GT2 Mamdani Fuzzy System
631(1)
11.6.3 Type-Reduction for a WH GT2 TSK Fuzzy System
632(2)
11.7 Defuzzification
634(3)
11.7.1 Approximation and Defuzzification
634(1)
11.7.2 End-Points Defuzzification
635(1)
11.7.3 Average of End-Points Defuzzification
636(1)
11.8 Summary
637(3)
11.8.1 WH GT2 Mamdani Fuzzy System that Uses Centroid Type-Reduction + Average of End-Points Defuzzification
638(1)
11.8.2 WH GT2 Mamdani Fuzzy System that Uses COS Type-Reduction + Average of End-Points Defuzzification
639(1)
11.8.3 Unnormalized A2-C0 WH GT2 TSK Fuzzy System
639(1)
11.8.4 Normalized A2-C0 WH GT2 TSK Fuzzy System
640(1)
11.9 Comprehensive Example
640(7)
11.10 Direct Defuzzification
647(3)
11.10.1 Proposed WH-NT Direct Defuzzification
647(2)
11.10.2 Proposed WH-BMM Direct Defuzzification
649(1)
11.11 Comprehensive Example Continued
650(1)
11.12 GT2 Fuzzy Basis Functions
651(4)
11.13 Remarks and Insights
655(2)
11.14 Designing WH GT2 Fuzzy Systems
657(7)
11.15 Applications
664(1)
11.16 Case Study: WH GT2 Fuzzy Logic Control
665(10)
11.16.1 What Is a GT2 FLC?
665(1)
11.16.2 System Description
666(1)
11.16.3 Controller Designs
667(1)
11.16.4 Simulation Results (WH GT2 FPID Versus IT2 FPID Versus T1 FPID and PID)
668(2)
Exercises
670(3)
References
673(2)
Index 675
Jerry M. Mendel received the Ph.D. degree in electrical engineering from the Polytechnic Institute of Brooklyn, Brooklyn, NY. Currently he is Professor of Electrical Engineering at the University of Southern California in Los Angeles. He has published over 570 technical papers and is author and/or co-author of 12 books, including Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Directions (Prentice-Hall, 2001), Perceptual Computing: Aiding People in Making Subjective Judgments (Wiley & IEEE Press, 2010), and Introduction to Type-2 Fuzzy Logic Control: Theory and Application (Wiley & IEEE Press, 2014). His present research interests include: type-2 fuzzy logic systems and their applications to a wide range of problems, including smart oil field technology, computing with words, and fuzzy set qualitative comparative analysis. He is a Life Fellow of the IEEE, a Distinguished Member of the IEEE Control Systems Society, and a Fellow of the International Fuzzy Systems Association. He was President of the IEEE Control Systems Society in 1986, a member of the Administrative Committee of the IEEE Computational Intelligence Society for nine years, and Chairman of its Fuzzy Systems Technical Committee and the Computing With Words Task Force of that TC. Among his awards are the 1983 Best Transactions Paper Award of the IEEE Geoscience and Remote Sensing Society, the 1992 Signal Processing Society Paper Award, the 2002 and 2014 Transactions on Fuzzy Systems Outstanding Paper Awards, a 1984 IEEE Centennial Medal, an IEEE Third Millenium Medal, and a Fuzzy Systems Pioneer Award (2008) from the IEEE Computational Intelligence Society. As of September 26, 2015, his publications have been cited (Google Scholar) more than 33,800 times.