Fuzzy logic and hydrological modeling

Title:

Personal Author:

Sen, Zekai

Publication Information:

Boca Raton, FL : CRC Press, 2010

Physical Description:

xi, 340 p. : ill. ; 24 cm.

ISBN:

9781439809396

Subject Term:

Hydrologic models -- Mathematics

Fuzzy logic

Spatial analysis (Statistics)

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010229058	GB656.2.H9 S46 2010	Open Access Book	Book	Searching... Unknown

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.

Author Notes

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

Preface	p. IX
About the Author	p. xi
Chapter 1 Introduction	p. 1
1.1 General	p. 1
1.2 Fuzziness in Hydrology	p. 4
1.3 Why Use Fuzzy Logic in Water Sciences?	p. 7
References	p. 10
Problems	p. 11
Chapter 2 Linguistic Variables and Logic	p. 13
2.1 General	p. 13
2.2 Words	p. 13
2.3 Linguistic Variables	p. 19
2.4 Scientific Sentences	p. 20
2.5 Fuzzy Scales	p. 21
2.5.1 Nominal Scale	p. 22
2.5.2 Ordinal Scale	p. 23
2.5.3 Interval Scale	p. 25
2.5.4 Ratio Scale	p. 25
2.6 Fuzzy Logic Thinking Stages	p. 27
2.7 Approximate Reasoning	p. 31
References	p. 32
Problems	p. 33
Chapter 3 Fuzzy Sets, Membership Functions, and Operations	p. 37
3.1 General	p. 37
3.2 Crisp and Fuzzy Sets in Hydrology	p. 38
3.3 Formal Fuzzy Sets	p. 55
3.4 Membership Functions	p. 57
3.4.1 Triangular	p. 58
3.4.2 Trapezium	p. 59
3.4.3 Sigmoid	p. 60
3.4.4 Probability Distributions	p. 61
3.4.5 Two-Piece Gaussian	p. 62
3.4.6 Generalized Bell Shape	p. 63
3.4.7 S-Shape	p. 64
3.4.8 Z-Shape	p. 65
3.5 Membership Function Allocation	p. 65
3.5.1 Subjective Grouping	p. 67
3.5.2 Objective Grouping	p. 69
3.6 Hedges (Adjectivized Words)	p. 71
3.6.1 Fuzzy Reduction (Contraction)	p. 72
3.6.2 Fuzzy Expansion (Dilatation)	p. 72
3.6.3 Fuzzy Reduction-Expansion (Intensification)	p. 73
3.7 Logical Operations on Fuzzy Sets	p. 74
3.7.1 Equivalance	p. 74
3.7.2 Containment	p. 74
3.7.3 "ANDing" (Intersection)	p. 75
3.7.4 "ORing" (Union)	p. 78
3.7.5 "NOTing" (Complement)	p. 80
3.7.6 De Morgan's Law	p. 82
3.7.7 Fuzzy Averaging	p. 84
References	p. 84
Problems	p. 85
Chapter 4 Fuzzy Numbers and Arithmetic	p. 91
4.1 General	p. 91
4.2 Fuzzy Numbers	p. 91
4.3 Fuzzy Addition	p. 95
4.4 Fuzzy Subtraction	p. 97
4.5 Fuzzy Multiplication	p. 99
4.5.1 Multiplication by a Constant	p. 101
4.6 Fuzzy Division	p. 102
4.6.1 Division by a Constant	p. 104
4.7 Extremes of Fuzzy Numbers	p. 105
4.8 Extension Principle	p. 108
References	p. 1ll
Problems	p. 1ll
Chapter 5 Fuzzy Associations and Clusters	p. 119
5.1 General	p. 119
5.2 Crisp to Fuzzy Relationships	p. 120
5.3 Logical Relationships	p. 123
5.4 Fuzzy Logic Relations	p. 125
5.5 Fuzzy Compositions	p. 134
5.6 Logical Categorization	p. 139
5.6.1 Logical Proportional Relation	p. 139
5.6.2 Logical Inverse Relation	p. 140
5.6.3 Logical Haphazard Relation	p. 141
5.6.4 Logical Extreme Cases	p. 142
5.6.5 Climate Classification	p. 143
5.7 Fuzzy Clustering Algorithms	p. 145
5.7.1 Distance Measure	p. 145
5.7.2 K-Means	p. 146
5.7.3 c-Means	p. 149
References	p. 158
Problems	p. 158
Chapter 6 Fuzzy Logical Rules	p. 163
6.1 General	p. 163
6.2 Fuzzification	p. 163
6.3 "if...Then..." Rules	p. 165
6.4 Fuzzy Proposition	p. 169
6.5 Input Rule Base Establishment	p. 178
6.5.1 Mechanical Documentation	p. 180
6.5.2 Personal Intuition	p. 182
6.5.3 Expert View	p. 182
6.5.4 Database Search	p. 183
6.5.4.1 Triggering	p. 183
6.5.4.2 Degree of Belief	p. 185
6.6 Complete Rule Base	p. 186
References	p. 189
Problems	p. 190
Chapter 7 FIS: Fuzzy Inference System	p. 195
7.1 General	p. 195
7.2 Fuzzy Inference Systems (FIS)	p. 196
7.3 Mamdani FIS	p. 199
7.4 Defuzzification	p. 203
7.4.1 Arithmetic Average	p. 205
7.4.2 Weighted Average	p. 206
7.4.3 Center of Gravity (Centroid)	p. 207
7.4.4 Smallest of Maxima	p. 207
7.4.5 Largest of Maxima	p. 208
7.4.6 Mean of the Range of Maxima	p. 208
7.4.7 Local Mean of Maxima	p. 209
7.5 Sugeno FIS	p. 210
7.6 Tsukamoto FIS	p. 214
7.7 Şen FIS	p. 215
7.8 FIS Training	p. 216
7.9 Triple Variable Fuzzy Systems	p. 237
7.10 Adaptive Network-Based FIS (ANFIS)	p. 220
7.10.1 Anfis Pitfalls	p. 223
References	p. 225
Problems	p. 226
Chapter 8 Fuzzy Modeling of Hydrological Cycle Elements	p. 229
8.1 General	p. 229
8.2 Simple Evaporation Modeling	p. 229
8.2.1 Evaporation Estimation by FIS	p. 231
8.3 Infiltration Rate Model	p. 235
8.4 Rainfall Amount Prediction	p. 241
8.4.1 Areal Rainfall Estimation	p. 247
8.5 Rainfall-Runoff Relationship	p. 251
8.5.1 Crisp Rainfall-Runoff Relationship	p. 252
8.5.2 Fuzzy Rainfall-Runoff Relationship	p. 253
8.6 Rainfall-Groundwater Recharge	p. 260
8.7 Fuzzy Aquifer Classification Chart	p. 262
8.8 River Traffic Model	p. 268
References	p. 273
Chapter 9 Fuzzy Water Resources Operation	p. 275
9.1 General	p. 275
9.2 Fuzzy Water Budget	p. 275
9.3 Drinking Water Consumption Prediction	p. 279
9.3.1 Data and Rule Base Sets	p. 281
9.4 Fuzzy Volume Change in Reservoir Storage	p. 289
9.5 Crisp and Fuzzy Dynamic Programming	p. 296
9.6 Multiple Reservoir Operation Rule	p. 302
9.7 Lake Level Estimation	p. 306
9.8 Triple Diagrams Rule Base	p. 311
9.9 Logical-Conceptual Models	p. 316
9.9.1 Conceptual Model of Fatnam System	p. 318
References	p. 322
Index	p. 325

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Author Notes

Table of Contents