ISBN-10:
1439809399
ISBN-13:
9781439809396
Pub. Date:
10/15/2009
Publisher:
Taylor & Francis
Fuzzy Logic and Hydrological Modeling / Edition 1

Fuzzy Logic and Hydrological Modeling / Edition 1

by Zekai Sen

Hardcover

Current price is , Original price is $210.0. You
Select a Purchase Option
  • purchase options
    $153.36 $210.00 Save 27% Current price is $153.36, Original price is $210. You Save 27%.
  • purchase options

Overview

Fuzzy Logic and Hydrological Modeling / Edition 1

The hydrological sciences typically present grey or fuzzy information, making them quite messy and a choice challenge for fuzzy logic application. Providing readers with the first book to cover fuzzy logic modeling as it relates to water science, the author takes an approach that incorporates verbal expert views and other parameters that allow him to eschew the use of mathematics. The book’s first seven chapters expose the fuzzy logic principles, processes and design for a fruitful inference system with many hydrological examples. The last two chapters present the use of those principles in larger scale hydrological scales within the hydrological cycle.

Product Details

ISBN-13: 9781439809396
Publisher: Taylor & Francis
Publication date: 10/15/2009
Pages: 348
Product dimensions: 6.12(w) x 9.25(h) x 0.90(d)

About the Author

Zekai Sen is a member of the Department of Civil Engineering at the Technical University of Istanbul.

Table of Contents

Preface IX

About the Author xi

Chapter 1 Introduction 1

1.1 General 1

1.2 Fuzziness in Hydrology 4

1.3 Why Use Fuzzy Logic in Water Sciences? 7

References 10

Problems 11

Chapter 2 Linguistic Variables and Logic 13

2.1 General 13

2.2 Words 13

2.3 Linguistic Variables 19

2.4 Scientific Sentences 20

2.5 Fuzzy Scales 21

2.5.1 Nominal Scale 22

2.5.2 Ordinal Scale 23

2.5.3 Interval Scale 25

2.5.4 Ratio Scale 25

2.6 Fuzzy Logic Thinking Stages 27

2.7 Approximate Reasoning 31

References 32

Problems 33

Chapter 3 Fuzzy Sets, Membership Functions, and Operations 37

3.1 General 37

3.2 Crisp and Fuzzy Sets in Hydrology 38

3.3 Formal Fuzzy Sets 55

3.4 Membership Functions 57

3.4.1 Triangular 58

3.4.2 Trapezium 59

3.4.3 Sigmoid 60

3.4.4 Probability Distributions 61

3.4.5 Two-Piece Gaussian 62

3.4.6 Generalized Bell Shape 63

3.4.7 S-Shape 64

3.4.8 Z-Shape 65

3.5 Membership Function Allocation 65

3.5.1 Subjective Grouping 67

3.5.2 Objective Grouping 69

3.6 Hedges (Adjectivized Words) 71

3.6.1 Fuzzy Reduction (Contraction) 72

3.6.2 Fuzzy Expansion (Dilatation) 72

3.6.3 Fuzzy Reduction-Expansion (Intensification) 73

3.7 Logical Operations on Fuzzy Sets 74

3.7.1 Equivalance 74

3.7.2 Containment 74

3.7.3 "ANDing" (Intersection) 75

3.7.4 "ORing" (Union) 78

3.7.5 "NOTing" (Complement) 80

3.7.6 De Morgan's Law 82

3.7.7 Fuzzy Averaging 84

References 84

Problems 85

Chapter 4 Fuzzy Numbers and Arithmetic 91

4.1 General 91

4.2 Fuzzy Numbers 91

4.3 Fuzzy Addition 95

4.4 Fuzzy Subtraction 97

4.5 Fuzzy Multiplication 99

4.5.1 Multiplication by a Constant 101

4.6 Fuzzy Division 102

4.6.1 Division by aConstant 104

4.7 Extremes of Fuzzy Numbers 105

4.8 Extension Principle 108

References 1ll

Problems 1ll

Chapter 5 Fuzzy Associations and Clusters 119

5.1 General 119

5.2 Crisp to Fuzzy Relationships 120

5.3 Logical Relationships 123

5.4 Fuzzy Logic Relations 125

5.5 Fuzzy Compositions 134

5.6 Logical Categorization 139

5.6.1 Logical Proportional Relation 139

5.6.2 Logical Inverse Relation 140

5.6.3 Logical Haphazard Relation 141

5.6.4 Logical Extreme Cases 142

5.6.5 Climate Classification 143

5.7 Fuzzy Clustering Algorithms 145

5.7.1 Distance Measure 145

5.7.2 K-Means 146

5.7.3 c-Means 149

References 158

Problems 158

Chapter 6 Fuzzy Logical Rules 163

6.1 General 163

6.2 Fuzzification 163

6.3 "if...Then..." Rules 165

6.4 Fuzzy Proposition 169

6.5 Input Rule Base Establishment 178

6.5.1 Mechanical Documentation 180

6.5.2 Personal Intuition 182

6.5.3 Expert View 182

6.5.4 Database Search 183

6.5.4.1 Triggering 183

6.5.4.2 Degree of Belief 185

6.6 Complete Rule Base 186

References 189

Problems 190

Chapter 7 FIS: Fuzzy Inference System 195

7.1 General 195

7.2 Fuzzy Inference Systems (FIS) 196

7.3 Mamdani FIS 199

7.4 Defuzzification 203

7.4.1 Arithmetic Average 205

7.4.2 Weighted Average 206

7.4.3 Center of Gravity (Centroid) 207

7.4.4 Smallest of Maxima 207

7.4.5 Largest of Maxima 208

7.4.6 Mean of the Range of Maxima 208

7.4.7 Local Mean of Maxima 209

7.5 Sugeno FIS 210

7.6 Tsukamoto FIS 214

7.7 Şen FIS 215

7.8 FIS Training 216

7.9 Triple Variable Fuzzy Systems 237

7.10 Adaptive Network-Based FIS (ANFIS) 220

7.10.1 Anfis Pitfalls 223

References 225

Problems 226

Chapter 8 Fuzzy Modeling of Hydrological Cycle Elements 229

8.1 General 229

8.2 Simple Evaporation Modeling 229

8.2.1 Evaporation Estimation by FIS 231

8.3 Infiltration Rate Model 235

8.4 Rainfall Amount Prediction 241

8.4.1 Areal Rainfall Estimation 247

8.5 Rainfall-Runoff Relationship 251

8.5.1 Crisp Rainfall-Runoff Relationship 252

8.5.2 Fuzzy Rainfall-Runoff Relationship 253

8.6 Rainfall-Groundwater Recharge 260

8.7 Fuzzy Aquifer Classification Chart 262

8.8 River Traffic Model 268

References 273

Chapter 9 Fuzzy Water Resources Operation 275

9.1 General 275

9.2 Fuzzy Water Budget 275

9.3 Drinking Water Consumption Prediction 279

9.3.1 Data and Rule Base Sets 281

9.4 Fuzzy Volume Change in Reservoir Storage 289

9.5 Crisp and Fuzzy Dynamic Programming 296

9.6 Multiple Reservoir Operation Rule 302

9.7 Lake Level Estimation 306

9.8 Triple Diagrams Rule Base 311

9.9 Logical-Conceptual Models 316

9.9.1 Conceptual Model of Fatnam System 318

References 322

Index 325

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews

Fuzzy Logic and Hydrological Modeling 5 out of 5 based on 0 ratings. 1 reviews.
Anonymous More than 1 year ago