Introduction to fuzzy methods: theory and application of fuzzy sets. 4., überarb. u. erw. Aufl.
(Einführung in Fuzzy-Methoden: Theorie und Anwendungen unscharfer Mengen.)

*(German)*Zbl 0771.94018Fuzzy set theory has increased to one of the most popular approaches to the cognitive modelling of vague data, inspired by its remarkable success in industrial applications of fuzzy control.

The present monograph introduces some important topics in this field, which are the foundations of fuzzy sets, fuzzy relations, approximate reasoning, fuzzy control, fuzzy measures, measures of fuzziness, and data analysis. In its contents the fourth edition has been revised and extended with respect to the previous ones. Revision especially refers to measure theoretical aspects while the incorporated extension is related to fuzzy data analysis, where qualitative and quantitative approaches as well as the valuation of methods are chosen to be considered.

The audience consists of mathematicians, but also practitioners of other disciplines like computer science and engineering, who are interested in the theoretical background of fuzzy methods.

It has to be emphasized that this book is one of the few German publications that fit the claim to a careful presentation of the foundation of fuzzy set theory.

It might be criticized that there are only few remarks regarding the crucial problems in handling fuzzy sets, namely, for example, the creation and interpretation of membership functions and the justification of fuzzy set operations. The essential fields of fuzzy control and approximate reasoning could have been investigated in more detail, whereas the chapter on data analysis reflects the actual state of the art.

The book is one of the best presentations of fuzzy methods that are available so far.

The present monograph introduces some important topics in this field, which are the foundations of fuzzy sets, fuzzy relations, approximate reasoning, fuzzy control, fuzzy measures, measures of fuzziness, and data analysis. In its contents the fourth edition has been revised and extended with respect to the previous ones. Revision especially refers to measure theoretical aspects while the incorporated extension is related to fuzzy data analysis, where qualitative and quantitative approaches as well as the valuation of methods are chosen to be considered.

The audience consists of mathematicians, but also practitioners of other disciplines like computer science and engineering, who are interested in the theoretical background of fuzzy methods.

It has to be emphasized that this book is one of the few German publications that fit the claim to a careful presentation of the foundation of fuzzy set theory.

It might be criticized that there are only few remarks regarding the crucial problems in handling fuzzy sets, namely, for example, the creation and interpretation of membership functions and the justification of fuzzy set operations. The essential fields of fuzzy control and approximate reasoning could have been investigated in more detail, whereas the chapter on data analysis reflects the actual state of the art.

The book is one of the best presentations of fuzzy methods that are available so far.

Reviewer: R.Kruse (Braunschweig)

##### MSC:

94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |

94-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory |

03E72 | Theory of fuzzy sets, etc. |