## Fuzzy sets and fuzzy decision-making.(English)Zbl 0864.90069

Boca Raton, FL: CRC Press. xi, 270 p. (1995).
The book presents some applications of fuzzy set theory to the management science. This branch of study is called ‘fuzzy decision making’. The book contains ten chapters. Chapter 1 provides a basic knowledge of fuzzy set theory. In my opinion this part should be based on many-valued logic because it is a natural starting point to decision making. Chapter 2 introduces the concept of factor spaces. This includes state spaces, operations and relations between factors, and concept ranking. Chapter 3 covers the basics of fuzzy decision making. By means of Zadeh’s extension principle, the feedback extension of a concept is proposed and made operational for decision making because of the capability of approximating the extension of a concept by its feedback extensions. Starting with a rough representation of the intension of a concept, the authors show that the intension of a concept can be represented by the extension of the concept, and vice versa. This establishes the basic framework of fuzzy decision making. Examples are given here. Chapter 4 provides many effective methods to the determination of membership functions. Chapter 5 introduces the concept of multifactorial analysis that is a basic tool in multifactorial fuzzy decision making. Chapter 6 is about the variable weights analysis where authors explore the principle of variable weights. Chapter 7 discusses multifactorial fuzzy decision making with multiple objectives. Chapter 8 studies the degree analysis based on set-valued statistics. Chapter 9 offers many effective methods for improving fuzzy operators that will enhance the effectiveness of fuzzy decision making. Chapter 10 introduces multifactorial fuzzy decision making based on Shafer’s theory of evidence.
In my opinion, the reviewed book is a competent and useful monograph devoted to the problem of fuzzy multifactorial decision making. On the other side it would have been good if the authors studied multifactorial decision making problems also from the point-view of Nakamuro’s fuzzy utility function. This is a very imported starting point to fuzzy decision making.

### MSC:

 90B50 Management decision making, including multiple objectives 03E72 Theory of fuzzy sets, etc.