The objective of Professor Negoita in this book is “to present the role of fuzzy systems in knowledge engineering so that it is accessible to a wide audience. . . .” The book is introductory and features many good examples. The 190 pages are divided into seven chapters. Each chapter has its own well-annotated bibliography. An appendix on Categorical Analysis of Logic is included at the end.

Chapter 1, the Introduction, is something like an executive overview; it covers a number of concepts that are dealt with in more depth in later chapters. It also presents some observations about the computer revolution and the impact of expert systems, as well as the use of fuzzy sets in representing vagueness. It ends in a brief historical note of how the concepts originated.

Chapter 2, Exact and Inexact Reasoning in Knowledge Representation, begins with a discussion of rules and inferences. Then it introduces the idea of “degrees of belief,” along with several ways of representing and propagating uncertainty. Next the theory of categories is introduced. I found this distracting because the reader is suddenly swamped with new nomenclature, diagrams, and concepts which are not defined very well.

Chapter 3, Fuzzy Sets, addresses the central issue: how to express and propagate vagueness with fuzzy sets. The reader is led into the subject from an intuitive standpoint--no theorems are stated or proved. The algebra is presented with a number of illustrations. The chapter ends with a short discussion of the category of fuzzy sets.

Chapter 4, Knowledge Representation, refers back to knowledge engineering and its use of production rules. Production rules and fuzzy sets are combined, and the reader is shown how to derive the fuzzy result of a production rule. The discussion on linguistic variables is good because of the examples.

Chapter 5, Approximate Reasoning, picks up where Chapter 4 left off and introduces the concepts of approximate reasoning and the use of truth variables. The knowledge diagrams introduced in the earlier chapters are next illustrated with examples. Finally, value questions and, very briefly, variable questions are discussed with some suggestion of predicate logic forms.

Chapter 6, Knowledge Engineering in Decision Support Systems, is the best chapter of the book. Although the examples are taken from a management decision context, they illustrate the ideas fairly well. It takes some doing to work through the examples and come up with the same results as in the book because the explanations are not as complete as they could be. Qualitative inquiries, linguistic variables, consequences of policy statements, and use of planning/forecasting with fuzzy dynamic models are the topics considered here.

Chapter 7, Knowledge Engineering in Management Expert Systems, returns to the use of production rules combined with linguistic variables, and it hedges in semantic systems. The idea of the use of verbal models to represent the domain experts’ knowledge is presented. This is similar to production rules; however, instead of IF-THEN statements, the knowledge is in the form of semantic statements about the elements and relationships (the vocabulary) of the domain of discourse. This, together with rewrite rules, initial conditions, and query statements, drives the inference process to respond with linguistic values, i.e., the answers.

In summary, this book’s material is for someone relatively new to the subject of fuzzy sets, or even new to expert systems. Hence, it presents the material in a conversational style. There are no proofs and no problem sets. It is good for the untrained reader. If further reading is to be done, the annotated references provide an excellent guide. However, the great deal of research work which has been done with fuzzy systems in control systems is not mentioned.

Other criticisms are as follows: (1) The use of analytical forms to express the membership functions instead of vectors or arrays (as is done in this book) is alluded to once but never developed. This makes the illustrations easier to understand but shortchanges the book’s completeness. (2) The author is convinced that the APL language is the one to use for this type of knowledge representation. This will immediately get the attention of LISP and PROLOG advocates. However, the material does not rely on APL syntax explicitly.

The book is interesting. It attempts to fulfill a current need. That need is for a book on the subject of fuzzy sets that provides a balance among rigor, clear explanations and examples, and problems (however “contrived”) for the reader.