Chapter 1 of this book contains some background on logic; t-norms and how they are used to define the conjunction operator for fuzzy sets; t-conorms and their use in defining the disjunctive operators; and phi-operators used as generalizations of implication. Chapter 2 is on the algebra of fuzzy sets and fuzzy relations, while chapter 3 covers fuzzy equations, systems of fuzzy equations, and their solvability. In chapter4, fuzzy controllers are discussed as the basis of fuzzy expert systems. Chapter 5 introduces metrics to measure the similarity of fuzzy models and sets.

I found the book to be dense, too formal, and short on examples or explanations. I would not recommend it for use in an undergraduate or graduate class as a primary textbook. Almost all of the material is presented in the definition-lemma-theorem-corollary format. The approach is mathematically rigorous, but it perpetuates the great sin of mathematicians--overformalizing at the expense of understanding. Even simple ideas that are intuitive and easy to explain can be obscured if we insist on a mathematically rigorous exposition. The book is not intended for someone who wants a gentle introduction to fuzzy systems. The reader should have a strong mathematical background to follow the book, and a neophyte in the field will have a lot of trouble reading it. The approach to fuzzy logic is from a mathematical point of view, as the title says. Applications of fuzzy logic are not described. The book is more of an exposition of the author’s research results than a balanced, thorough overview of the field. I would recommend the book only to researchers who want to engage in theoretical work in fuzzy logic.