## Table of Contents

Introduction

General

Fuzziness in Hydrology

Why Use Fuzzy Logic in Water Sciences?

References

Problems

Linguistic Variables and Logic

General

Words

Linguistic Variables

Scientific Sentences

Fuzzy Scales

Fuzzy Logic Thinking Stages

Approximate Reasoning

References

Problems

Fuzzy Sets, Membership Functions, and Operations

General

Crisp and Fuzzy Sets in Hydrology

Formal Fuzzy Sets

Membership Functions

Membership Function Allocation

Hedges (Adjectivized Words)

Logical Operations on Fuzzy Sets

References

Problems

Fuzzy Numbers and Arithmetics

General

Fuzzy Numbers

Fuzzy Addition

Fuzzy Subtraction

Fuzzy Multiplication

Fuzzy Division

Extremes of Fuzzy Numbers

Extension Principle

References

Problems

Fuzzy Associations and Clusters

General

Crisp to Fuzzy Relationships

Logical Relationships

Fuzzy Logic Relations

Fuzzy Compositions

Logical Categorization

Fuzzy Clustering Algorithms

References

Problems

Fuzzy Logical Rules

General

Fuzzification

“IF . . . THEN . . .” Rules

Fuzzy Proposition

Input Rule Base Establishment

Complete Rule Base

References

Problems

FIS

General

Fuzzy Inference Systems (FIS)

Mamdani FIS

Defuzzification

Sugeno FIS

Tsukamoto FIS

S¸ en FIS

FIS Training

Triple Variable Fuzzy Systems

Adaptive-Network-Based FIS (ANFIS)

References

Problems

Fuzzy Modeling of Hydrological Cycle Elements

General

Simple Evaporation Modeling

Infiltration Rate Model

Rainfall Amount Prediction

Rainfall–Runoff Relationship

Rainfall–Groundwater Recharge

Fuzzy Aquifer Classification Chart

River Traffic Model

References

Fuzzy Water Resources Operation

General

Fuzzy Water Budget

Drinking Water Consumption Prediction

Fuzzy Volume Change in Reservoir Storage

Crisp and Fuzzy Dynamic Programming

Multiple Reservoir Operation Rule

Lake Level Estimation

Triple Diagrams Rule Base

Logical-Conceptual Models

References