Review of Fuzzy Logic and Hydrological Modeling by Zekâi Şen: CRC Press, Taylor & Francis Group, Boca Raton, FL; 2010; ISBN 978-1-4398-0939-6; 340 pp.

 When addressing a hydrologic problem, the author states in the preface of the book, “basic linguistic knowledge, experience, and expert views help establish the preliminary skeleton of the solution, which may later be supported by the numerical data.” He goes on to say: “In almost every corner, hydrological sciences have gray fore- and backgrounds with verbal information. The big dilemma is how to deal with gray information for arriving at decisive conclusions with crisp and deterministic principles. Fuzzy logic (FL) principles with linguistically valid propositions and vague categorization provide a sound background for the evaluation of such information.” Put another way, for solving any hydrological problem, along with data, expert knowledge in the form of logic or experience-based information is often important, but it is difficult to code this information into mathematical equations; fuzzy logic offers a way to make use of this information. Thus, the main focus of the book, as stated by the author, is “to prepare the reader with linguistic (verbal) qualitative data interpretation and treatment procedures on the basis of FL principles.”

The subject matter of book is divided into nine chapters, with the first seven chapters presenting an expository account of the FL principles and the remaining two chapters discussing applications. The first chapter introduces fuzzy logic and discusses the origin thereof, and goes on to explain the concept of fuzziness in hydrology and why fuzzy logic can help solve hydrological questions. The discussion distinguishes between the concepts of “stochastic uncertainty” and “fuzziness” as they apply to real-world hydrologic processes.

Linguistic variables and logic constitute the subject matter of Chapter 2, explaining the fuzzy content of words, adjectives, and sentences in describing human thought or a particular condition or state thereof. It is argued that this state leads to the use of concepts, which if represented on a measuring scale, will not be totally definite and would have gray or fuzzy zones. The fuzziness involved in the thought process and reasoning is then discussed.

Chapter 3 deals with the concept of fuzzy sets, membership functions, and operations. The meaning of crisp and fuzzy sets in hydrology is discussed, using illustrative examples. The examples are based on discharge, drought, drinking water quality, soil types, rainfall measurements, drainage basin, and groundwater. The discussion also sheds light on how fuzziness can be reduced or increased or intensified, and introduces the logical operations employed on fuzzy sets.

Fuzzy numbers and arithmetic are presented in Chapter 4. Included in the arithmetic operations are fuzzy addition, fuzzy subtraction, fuzzy multiplication, fuzzy division, extremes of fuzzy numbers, and extension principle. Each operation is illustrated with examples from hydrology.

Chapter 5 discusses the concept of association and clusters. Differences between logical relationships and fuzzy logic relationships with different sets of variables are clearly made. The importance of the relationship between different variables is also explained and three clustering algorithms—namely, distance measure, k-means, and c-means—are discussed with examples.

Fuzzy logical rules are presented in chapter 6. Explaining the rational and logical difference between classical logic and fuzzy logic, a description of how linguistic input and output variables are identified and decomposed into formal fuzzy subsets is given, followed by the use of “if … then …” rules. The last part of the chapter deals with rule-based establishment and discusses the need for mechanical documentation, when information about the phenomenon studied is not available, expert opinion to refine the modeling exercise, use of data, and degrees of belief.

Chapter 7 discusses fuzzy inference systems (FIS), and highlights the important elements in a fuzzy expert system and explains the merits and differences between the Mamdani FIS, Sugeno FIS, Tsukamoto FIS, and Şen FIS. It also deals with defuzzification, FIS training, triple variable fuzzy systems, and adaptive network-based FIS and its drawbacks.

Chapters 8 and 9 deal with the application of fuzzy modeling of hydrological processes and water resources system operations, respectively. They present examples of applications to virtually every component of the hydrological cycle, including evaporation, infiltration, rainfall prediction, and groundwater recharge. A section on river traffic modeling is also included. In the discussion of water resources system operation are included water budget, prediction of drinking water consumption, and reservoir management and operation rules.

To summarize, chapters 1–7 include a set of problems and exercises that may help the reader with the comprehension of concepts. The author makes extensive use of examples throughout the different chapters to illustrate concepts and their application in the field of hydrology and water resources. Although relevant, the list of references does not seem to be exhaustive. Early works done on this subject are well represented, while works done in the past ten years are generally scanty in the list. This omission does not help the reader in gaining a complete picture of the application of fuzzy logic in hydrology and water resources management.

The book is well written, sections are organized in a coherent manner with a natural flow from basic to more advanced concepts, and concludes with illustrative applications. This is probably the first book on the subject of fuzzy logic in hydrology, and Dr. Şen should be commended for this valuable contribution to the hydrologic literature. The book would be a valuable tool for senior undergraduate students or beginning graduate students in civil and agricultural engineering, earth and watershed sciences, or environmental sciences. For researchers in the field, it can also be a valuable addition to their library.