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Reviewer: Herbert Toth

According to the publisher, this book “provides a complete and coherent theory of adaptive neurofuzzy algorithms for both on-line and off-line modelling and control of unknown, nonlinear, dynamic processes.” By keeping computational aspects in mind, the book not only provides a rich source of theoretical results, but is of great use for industrial researchers implementing neurofuzzy algorithms, since the authors demonstrate the interrelationships between several approaches and explain their merits and disadvantages. For both fuzzyists and neuralists, it is useful, if not necessary, to have some knowledge about the other area in order to gain the most from this book. While reading the book, I felt that it is more for neuralists who want to learn about the connections of neural networks and fuzzy control; it is harder to read for an average fuzzyist who, usually, knows only a little about the many special network models. The book is divided into a preface, 11 chapters, a long bibliography, five appendices, and a three-page index. Throughout, a lot of well-designed and well-chosen figures enhance the intelligibility of the text. All chapters start with an overview and close with a section devoted to a summary or discussion of the chapters contents. This is enormously helpful for the reader in getting through the many pieces of knowledge provided, and in recognizing the interconnections between them. The book focuses on the learning, modeling, and representational abilities of certain types of associative memory networks (AMNs), which are based on a three layer architecture, in which the input layer provides a fixed nonlinear mapping of the sensor-based input space to a higher dimensional associative layer composed of compact support functions. The output of the hidden layer is linearly transformed by an adaptive weight vector (or equivalently by beliefs or confidences for a fuzzy network) and this linear dependence on a set of adjustable parameters means that convergence conditions can be established and the rate of convergence can be directly related to the condition of the networks basis functions (p. xii). Chapter 1, “An Introduction to Learning Modelling and Control,” gives a rough overview of the main topics of the book, and a condensed description of its main stream of argumentation and results. Chapter 2, “Neural Networks for Modelling and Control,” offers general introductory information about the concepts and network models used later in the book. Chapters 3 through 5, “Associative Memory Networks,” “Adaptive Linear Modelling,” and “Instantaneous Learning Algorithms,” describe the relevant types of AMNs within a common framework, and propose and investigate learning rules for these networks. Three network types are described in detail: Albuss cerebellar model articulation controller (CMAC), the B-spline network, and certain kinds of fuzzy systems. Chapter 6, “The CMAC Algorithm,” and chapter 7, “The Modelling Capabilities of the Binary CMAC,” describe the features of this class of algorithms. Chapter 8, “Adaptive B-spline Networks,” provides a concise and self-contained introduction to the B-spline network. Two algorithms for automatically determining the B-splines structure from a data set are described. They make this kind of network applicable to poorly understood problems when there is enough training data. Chapter 9, “B-spline Guidance Algorithms,” presents two B-spline applications. Chapter 10, “The Representation of Fuzzy Algorithms,” analyzes the properties of fuzzy systems and shows that they are members of the class of AMNs. Chapter 11, “Adaptive Fuzzy Modelling and Control,” illustrates the application of neurofuzzy algorithms to adaptive modeling and control schemes. All in all, this book is an interesting and valuable contribution to intelligent control. I thus recommend it to everyone who is interested in the newest developments in this field.