Modeling Uncertainty with Fuzzy Logic: With Recent Theory and Applications / Edition 1

Modeling Uncertainty with Fuzzy Logic: With Recent Theory and Applications / Edition 1

by Asli Celikyilmaz, Burhan T?rksen
     
 

ISBN-10: 3642100635

ISBN-13: 9783642100635

Pub. Date: 12/15/2010

Publisher: Springer Berlin Heidelberg

The series "Studies in Fuzziness and Soft Computing" contains publications on various areas within the so-called soft computing which include fuzzy sets, rough sets, neural networks, evolutionary computations, probabilistic and evidential reasoning, multi-valued logic, and related fields. The publications within "Studies in Fuzziness and Soft Computing" are

…  See more details below

Overview

The series "Studies in Fuzziness and Soft Computing" contains publications on various areas within the so-called soft computing which include fuzzy sets, rough sets, neural networks, evolutionary computations, probabilistic and evidential reasoning, multi-valued logic, and related fields. The publications within "Studies in Fuzziness and Soft Computing" are primarily monographs and edited volumes. They cover significant recent developments in the field, both of a foundational and applicable character. An important feature of the series is its short publication time and world-wide distribution. This permits a rapid and broad dissemination of research results.

The objective of this book is to present an uncertainty modeling approach using a new type of fuzzy system model via "Fuzzy Functions". Since most researchers on fuzzy systems are more familiar with the standard fuzzy rule bases and their inference system structures, many standard tools of fuzzy system modeling approaches are reviewed to demonstrate the novelty of the structurally different fuzzy functions, before we introduced the new methodologies. To make the discussions more accessible, no special fuzzy logic and system modeling knowledge is assumed. Therefore, the book itself may be a reference for some related methodologies to most researchers on fuzzy systems analyses. For those readers, who have knowledge of essential fuzzy theories, Chapter 1, 2 should be treated as a review material. Advanced readers ought to be able to read chapters 3, 4 and 5 directly, where proposed methods are presented. Chapter 6 demonstrates experiments conducted on various datasets.

Read More

Product Details

ISBN-13:
9783642100635
Publisher:
Springer Berlin Heidelberg
Publication date:
12/15/2010
Series:
Studies in Fuzziness and Soft Computing Series, #240
Edition description:
Softcover reprint of hardcover 1st ed. 2009
Pages:
400
Product dimensions:
6.14(w) x 9.21(h) x 0.91(d)

Table of Contents

1 Introduction 1

1.1 Motivation 1

1.2 Contents of the Book 3

1.3 Outline of the Book 9

2 Fuzzy Sets and Systems 11

2.1 Introduction 11

2.2 Type-1 Fuzzy Sets and Fuzzy Logic 12

2.2.1 Characteristics of Fuzzy Sets 13

2.2.2 Operations on Fuzzy Sets 14

2.3 Fuzzy Logic 18

2.3.1 Structure of Classical Logic Theory 18

2.3.2 Relation of Set and Logic Theory 19

2.3.3 Structure of Fuzzy Logic 19

2.3.4 Approximate Reasoning 21

2.4 Fuzzy Relations 22

2.4.1 Operations on Fuzzy Relations 25

2.4.2 Extension Principle 25

2.5 Type-2 Fuzzy Sets 28

2.5.1 Type-2 Fuzzy Sets 29

2.5.2 Interval Valued Type-2 Fuzzy Sets 31

2.5.3 Type-2 Fuzzy Set Operations 32

2.6 Fuzzy Functions 33

2.7 Fuzzy Systems 36

2.8 Extensions of Takagi-Sugeno Fuzzy Inference Systems 40

2.8.1 Adaptive-Network-Based Fuzzy Inference System (ANFIS) 41

2.8.2 Dynamically Evolving Neuro-Fuzzy Inference Method (DENFIS) 44

2.8.3 Genetic Fuzzy Systems (GFS) 46

2.9 Summary 50

3 Improved Fuzzy Clustering 51

3.1 Introduction 51

3.2 Fuzzy Clustering Algorithms 52

3.2.1 Fuzzy C-Means Clustering Algorithm 53

3.2.2 Classification of Objective Based Fuzzy Clustering Algorithms 58

3.2.3 Fuzzy C-Regression Model (FCRM) Clustering Algorithm 58

3.2.4 Variations of Combined Fuzzy Clustering Algorithms 61

3.3 Improved Fuzzy Clustering Algorithm (IFC) 64

3.3.1 Motivation 64

3.3.2 Improved Fuzzy Clustering Algorithm for Regression Models (IFC) 69

3.3.3 Improved Fuzzy Clustering Algorithm for Classification Models (IFC-C) 73

3.3.4 Justification of Membership Values of the IFC Algorithm 77

3.4 Two New Cluster Validity Indices for IFC and IFC-C 85

3.4.1 Overview of Well-Known ClusterValidity Indices 86

3.4.2 The New Cluster Validity Indices 90

3.4.3 Simulation Experiments [Celikyilmaz and Turksen, 2007i;2008c] 94

3.4.4 Discussions on Performances of New Cluster Validity Indices Using Simulation Experiments 100

3.5 Summary 103

4 Fuzzy Functions Approach 105

4.1 Introduction 105

4.2 Motivation 107

4.3 Proposed Type-1 Fuzzy Functions Approach Using FCM - T1FF 112

4.3.1 Structure Identification of FF for Regression Models (T1FF) 112

4.3.2 Structure Identification of the Fuzzy Functions for Classification Models (T1FF-C) 119

4.3.3 Inference Mechanism of T1FF for Regression Models 121

4.3.4 Inference Mechanism of T1FF for Classification Models 122

4.4 Proposed Type-1 Improved Fuzzy Functions with IFC - T1IFF 125

4.4.1 Structure Identification of T1IFF for Regression Models 125

4.4.2 Structure Identification of T1IFF-C for Classification Models 131

4.4.3 Inference Mechanism of T1IFF for Regression Problems 132

4.4.4 Inference with T1IFF-C for Classification Problems 135

4.5 Proposed Evolutionary Type-1 Improved Fuzzy Function Systems 136

4.5.1 Genetic Learning Process: Genetic Tuning of Improved Membership Functions and Improved Fuzzy Functions 139

4.5.2 Inference Method for ET1IFF and ET1IFF-C 145

4.5.3 Reduction of Structure Identification Steps of T1IFF Using the Proposed ET1IFF Method 146

4.6 Summary 147

5 Modeling Uncertainty with Improved Fuzzy Functions 149

5.1 Motivation 149

5.2 Uncertainty 154

5.3 Conventional Type-2 Fuzzy Systems 157

5.3.1 Generalized Type-2 Fuzzy Rule Bases Systems (GT2FRB) 157

5.3.2 Interval Valued Type-2 Fuzzy Rule Bases Systems (IT2FRB) 160

5.3.3 Most Common Type-Reduction Methods 162

5.3.4 Discrete Interval Type-2 Fuzzy Rule Bases (DIT2FRB) 164

5.4 Discrete Interval Type-2 Improved Fuzzy Functions 167

5.4.1 Background of Type-2 Improved Fuzzy Functions Approaches 168

5.4.2 Discrete Interval Type-2 Improved Fuzzy Functions System (DIT2IFF) 179

5.5 The Advantages of Uncertainty Modeling 193

5.6 Discrete Interval Type-2 Improved Fuzzy Functions with Evolutionary Algrithms 196

5.6.1 Motivation 196

5.6.2 Architecture of the Evolutionary Type-2 Improved Fuzzy Functions 197

5.6.3 Reduction of Structure Identification Steps of DIT2IFF Using New EDIT2IFF Method 213

5.7 Summary 215

6 Experiments 217

6.1 Experimental Setup 217

6.1.1 Overview of Experiments 217

6.1.2 Three-Way Sub-sampling Cross Validation Method 219

6.1.3 Measuring Models' Prediction Performance 221

6.1.3.1 Performance Evaluations of Regression Experiments 221

6.1.3.2 Performance Evaluations of Classification Experiments 223

6.2 Parameters of Benchmark Algorithms 227

6.2.1 Support Vector Machines (SVM) 228

6.2.2 Artificial Neural Networks (NN) 229

6.2.3 Adaptive-Network-Based Fuzzy Inference System (ANFIS) 229

6.2.4 Dynamically Evolving Neuro-Fuzzy Inference Method (DENFIS) 231

6.2.5 Discrete Interval Valued Type-2 Fuzzy Rule Base (DIT2FRB) 231

6.2.6 Genetic Fuzzy System (GFS) 232

6.2.7 Logistic Regression, LR, Fuzzy K-Nearest Neighbor, FKNN 234

6.3 Parameters of Proposed Fuzzy Functions Algorithms 234

6.3.1 Fuzzy Functions Methods 234

6.3.2 Imporoved Fuzzy Functions Methods 236

6.4 Analysis of Experiments - Regression Domain 238

6.4.1 Friedman's Artificial Domain 238

6.4.2 Auto-mileage Dataset 245

6.4.3 Desulphurization Process Dataset 251

6.4.4 Stock Price Analysis 262

6.4.5 Proposed Fuzzy Cluster Validity Index Analysis for Regression 276

6.5 Analysis of Experiments - Classification (Pattern Recognition) Domains 278

6.5.1 Classification Datasets from UCI Repository 279

6.5.2 Classification Dataset from StatLib 281

6.5.3 Results from Classification Datasets 281

6.5.4 Proposed Fuzzy Cluster Validity Index Analysis for Classification 283

6.5.5 Performance Comparison Based on Elapsed Times 284

6.6 Overall Discussions on Experiments 289

6.6.1 Overall Comparison of System Modeling Methods on Regression Datasets 290

6.6.2 Overall Comparison of System Modeling Methods on Classification Datasets 297

6.7 Summary of Results and Discussions 300

7 Conclusions and Future Work 305

7.1 General Conclusions 305

7.2 Future Work 310

References 313

Appendix 321

A.1 Set and Logic Theory - Additional Information 321

A.2 Fuzzy Relations (Composition) - An Example 322

B.1 Proof of Fuzzy c-Means Clustering Algorithm 323

B.2 Proof of Improved Fuzzy Clustering Algorithm 326

C.1 Artificial Neural Networks ANNs) 327

C.2 Support Vector Machines 329

C.3 Genetic Algorithms 338

C.4 Multiple Linear Regression Algorithms with Least Squares Estimation 340

C.5 Logistic Regression 341

C.6 Fuzzy K-Nearest Neighbor Approach 343

D.1 T-Test Formula 344

D.2 Friedman's Artificial Dataset: Summary of Results 345

D.3 Auto-mileage Dataset: Summary of Results 354

D.4 Desulphurization Dataset: Summary of Results 363

D.5 Stock Price Datasets: Summary of Results 367

D.6 Classification Datasets: Summary of Results 388

D.7 Cluster Validity Index Graphs 397

D.8 Classification Datasets - ROC Graphs 398

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >