Data scientists are mainly required to extract valuable knowledge from data. To this end, intelligent systems are often designed for knowledge extraction and representation. This poses a number of challenges, including the ability of end users to fully understand the acquired knowledge. This is the core of Cpałka’s book, which is mainly focused on fuzzy rule-based systems.

Getting intelligent systems into widespread real-world use requires careful design choices, not only from the point of view of performance, but also in recently recognized features such as transparency and accountability [1]. In particular, interpretability is the quality of systems to provide end users with knowledge that is easy to read and understand. Interpretability is important to enable interaction of machines with humans; thus, it is a necessary condition for collaborative intelligence.

Fuzzy logic is deemed a good candidate for the mathematical underpinning onto which intelligent and interpretable systems can be designed. In particular, with fuzzy logic knowledge can be endowed with a semantics that is of a perceptual nature (that is, the meanings of concepts do not have rigid and arbitrary bounds) similar to the semantics of natural language terms. As a consequence, the knowledge acquired through fuzzy systems (usually rule based) can be expressed as simplified natural language sentences that can be used in approximate reasoning schemes, which take into account the gradualness and granularity of knowledge to infer new knowledge that can be easily reported to non-technically skilled people.

A knowledge base designed on interpretability principles is more constrained than another designed based on performance criteria only. This requires some design tradeoffs, while the development of methods trying to harmonize interpretability with other important features (such as predictive accuracy) is a matter of current scientific research. In this scenario, Cpałka’s book presents a possible methodology to achieve good performances of interpretable fuzzy systems by exploiting the immense flexibility that is granted by the use of fuzzy logic.

In fact, whereas in traditional logic there is one way only to define a logical operator (for example, conjunction, implication, and so on), in fuzzy logic there are infinite possibilities, and in many cases parametric operators can be used. In this way, while keeping the symbolic description of an operator (for example, “AND”), it is possible to vary its semantics in order to better adapt to available data. This is the overall approach followed by the book: after a short introduction on fuzzy systems design (chapter 1) and interpretability (chapter 2), the author introduces the concept of the flexible fuzzy system (chapter 3), which uses a highly parametric structure of fuzzy rules, which preserve a unique symbolic description with linguistic terms. Training of flexible fuzzy systems is the subject of chapter 4, where gradient-based approaches are presented; in chapter 5, an evolutionary learning approach is reported for data-driven design. The subsequent chapters illustrate two real-world case studies in fuzzy control and identity verification.

It must be said that, even if the title of the book promises a general treatment on the design of interpretable fuzzy systems, the book actually offers a very partial view of the subject, which is confined to a specific methodology that is the result of the research efforts of its author. There are many arguments that are left apart, from the foundations of the concept of interpretability up to the dozens of methods that can be used to design interpretable fuzzy systems. Also, there is no mention of the recent evolution of research on interpretability into the more general topic of explainable artificial intelligence. As a consequence, although the book is valuable as a thorough reference for the design of flexible fuzzy systems, it lacks a comprehensive treatment on interpretability and design of interpretable fuzzy models, for which the reader must still rely on older books and papers available in the scientific literature.