Teaching fuzzy logic in undergraduate courses has become quite popular due to the increasing number of successful applications in many areas, including control, system identification, decision making, knowledge discovery, and so on. As a result, the number of textbooks on fuzzy logic has increased in the last decade. Furthermore, the 50th anniversary of the publication of the first paper on fuzzy logic [1], by Lotfi Zadeh, falls in 2015, and a number of initiatives have been undertaken to honor this event. The authors celebrate this anniversary by presenting a new textbook on fuzzy logic for engineering students.

The book is slim: it compresses all the key concepts of fuzzy logic in about 200 pages. It is structured in eight chapters, spanning the essential topics of fuzzy logic (fuzzy sets and their algebra, fuzzy relations, fuzzy inference, fuzzy measures, fuzzy arithmetic, and so on), but only the last chapter deals with a typical engineering problem, namely fuzzy control. Therefore, the book would be well suited for introductory courses in other disciplines including computer science.

The authors’ approach to introducing fuzzy logic is quite innovative and different. In particular, the authors start their arguments from the philosophical roots of the theory. As an example, instead of presenting fuzzy sets as is usually done, that is, as extensions of classical (crisp) sets, the authors start with some arguments based on Wittgenstein’s concept of language games and, on this basis, develop a mathematical model that gives rise to the definition of fuzzy sets in terms of membership functions. In the same way, when introducing reasoning with fuzzy logic, the authors first present a very abstract metamathematical model that accommodates different forms of reasoning (conjectural, deductive, abductive, speculative), and then derive the usual fuzzy reasoning rules like generalized modus ponens. I really appreciated how the the basic concepts are presented starting from their roots, because it obviates possible misunderstandings (like the confusion between fuzzy logic and probability theory) that could undermine a genuine understanding of fuzzy logic. This is another argument in favor of a wider audience than just engineering students.

The structure of each chapter is conversational: each argument is presented in terms of its key ideas, and then formalized and exemplified with simple examples. Short proofs of main theorems are provided. Although the book is full of mathematical formulas, it is not as heavy as a book on mathematical fuzzy logic. It is smooth to read, but it cannot be used like a handbook--the chapters require a sequential study because each of them is based on concepts and symbols discussed in previous chapters. Also, there is no index and the bibliography is not rich. Overall, the book shows an appreciable coherency of formalism and argumentation, with few exceptions (for example, I did not like the presentation of fuzzy partitions in the first chapter because the orthogonality requirement of fuzzy partitions cannot be applied to fuzzy sets generically defined on lattices, the chapter’s core argument).

The book doesn’t have exercises--a flaw in a book intended for students. Also, many examples are quite abstract, while other books targeted at the same audience offer a plethora of concrete examples and exercises (for example, Ross’ monograph [2]). However, even with these gaps, the approach taken by the authors to explain fuzzy logic makes me strongly recommend it for basic undergraduate and graduate courses on fuzzy logic or soft computing.