Data engineering : fuzzy mathematics in systems theory and data analysis / Olaf Wolkenhauer.

Format:

Book

Author/Creator:

Wolkenhauer, Olaf, 1966-

Language:

English

Subjects (All):

Database management.

Fuzzy systems.

System analysis.

Physical Description:

xxxii, 263 pages : illustrations ; 25 cm

Place of Publication:

New York : Wiley, [2001]

Summary:

Although data engineering is a multi-disciplinary field with applications in control, decision theory, and the emerging hot area of bioinformatics, there are no books on the market that make the subject accessible to non-experts. This book fills the gap in the field, offering a clear, user-friendly introduction to the main theoretical and practical tools for analyzing complex systems. An ftp site features the corresponding MATLAB and Mathematical tools and simulations. Market: Researchers in data management, electrical engineering, computer science, and life sciences.

Contents:

1 System Analysis 1

1.1 Uncertainty 5

1.2 The Art of Modelling: Linkage 5

1.3 Dynamic Systems 15

1.4 Example: Coupled Tanks Model 28

2 Uncertainty Techniques 31

2.1 The Least-Squares Criterion 36

2.1.1 Example: Regression Line 44

2.1.2 Example: Fourier Series 46

2.2 Maximum Likelihood Estimation 50

2.2.1 Example: ML-Estimates 51

2.2.2 The EM Algorithm 52

2.3 Stochastic Processes 53

2.3.1 Example: Kalman-Bucy Filtering 62

3 Learning from Data: System Identification 69

3.1 The Probabilistic Perspective 72

3.2 Kernel Density Estimation 75

3.3 Basis Function Approximation 77

3.4 Example: EM Algorithm 78

3.5 Discussion: Modelling and Identification 81

4 Propositions as Subsets of the Data Space 83

4.1 Hard-c-Means Clustering 87

4.2 Least-Squares Functionals: Fuzzy Clustering 89

4.3 Example: Hard vs. Fuzzy Clustering 94

4.4 Orthogonal Transformation 95

4.5 Example: Classification 99

4.6 Similarity-Based Reasoning 104

4.7 The Quotient Induced by Similarity Relations 106

5 Fuzzy Systems and Identification 109

5.1 Fuzzy Systems Model Structures 112

5.2 Identification of Antecedent Fuzzy Sets 114

5.3 Parameter Identification in the Takagi-Sugeno Model 116

5.4 Example: TS-Modelling and Identification 117

5.5 Example: Prediction of a Chaotic Time-Series 120

5.7 Regression Models and Fuzzy Clustering 124

5.8 Example: pH Neutralization Process 126

6 Random-Set Modelling and Identification 129

6.1 Random Variables, Point-Valued Maps 130

6.2 Random-Sets, Multi-Valued Maps 132

6.3 A Random-Set Approach to System Identification 135

6.4 Example 1: Nonlinear AR Process 139

6.5 Example 2: Box-Jenkins Gas-Furnace Data 142

7 Certain Uncertainty 145

7.1 Uncertainty in Systems Analysis 151

7.2 A Fuzzy Propositional Calculus 152

7.2.1 Probabilistic Logic 154

7.2.2 Classical Two-Valued Logic 154

7.2.3 Approximate Reasoning 156

8 Fuzzy Inference Engines 161

8.1 Composition-Based Inference 162

8.2 Individual-Rule-Based Inference 163

8.3 Fuzzy Systems as Nonlinear Mappings 166

8.4 Example: Comparison of Inference Engines 168

9 Fuzzy Classification 173

9.1 Equivalence of Fuzzy and Statistical Classifiers 173

9.2 Fuzzy Rule-Based Classifier Design 176

10 Fuzzy Control 181

10.1 PI-Control vs. Fuzzy PI-Control 182

10.2 Example 1: First-Order System with Dead-Time 187

10.3 Example 2: Coupled Tanks 192

11 Fuzzy Mathematics 197

11.1 The Algebra of Fuzzy Sets 201

11.2 The Extension Principle 202

11.3 Fuzzy Rules and Fuzzy Graphs 204

11.4 Fuzzy Logic 205

11.5 A Bijective Probability - Possibility Transformation 206

11.6 Example: Maintenance Decision Making 208

11.7 Example: Evaluating Student Performances 210

12.1 System Representations 213

12.2 More Philosophical Ideas 223

12.2.1 Data Engineering 227

13.1 Sets, Relations, Mappings 231

13.2 Measuring Forecast Accuracy 238

13.3 (Hierarchical) Clustering 239

13.4 Measure Spaces and Integrals 240

13.5 Unbiasedness of Estimators 245

13.6 Statistical Reasoning 246

13.7 Frequency Analysis 248.

Notes:

"A Wiley-Interscience publication."

Includes bibliographical references (p. 252-254) and index.

ISBN:

0471416568

OCLC:

47183703