##
**Fuzzy sets, fuzzy logic, fuzzy methods with applications.**
*(English)*
Zbl 0833.94028

Chichester: Wiley. x, 239 p. (1995).

The book is the English version of the fourth, revised and expanded German version of the book issued first in 1990 (Berlin Akademie Verlag; see the reviews in Zbl 0688.94006 and Zbl 0771.94018).

The present book introduces the basic notions of fuzzy sets in a mathematically firm manner. But it also treats them in relation to their essential applications. And the principles of such applications are explained too.

The first, introductory chapter deals with the intuitive and mathematical comparison of the basic concepts of fuzzy sets and crisp (common) sets as well as with the main references concerning the development of the theory and application of the fuzzy field of mathematics.

In the second chapter the theory of fuzzy sets in fully treated from the definition of fuzzy set to the integrating fuzzy functions over fuzzy domain – including the operations to and functions of fuzzy sets and fuzzy numbers, as well as fuzzy arithmetic. The third chapter deals with the fuzzified relationships and properties of fuzzy relations.

In the fourth chapter the linguistic variables and their applications are treated including fuzzy control and approximate reasoning and their applications. The fifth chapter deals with the measure theory in connection with fuzzy sets. Fuzzy measures for crisp and fuzzy sets including fuzzy integrals, probability concepts, applications and the measures of fuzziness are also introduced and discussed.

The sixth chapter’s topic is the fuzzy data analysis including the qualitative and quantitative ones, as well as fuzzy inference.

The book is closed by a full bibliography (more than 300 entries on 18 pages) and an index.

The present book introduces the basic notions of fuzzy sets in a mathematically firm manner. But it also treats them in relation to their essential applications. And the principles of such applications are explained too.

The first, introductory chapter deals with the intuitive and mathematical comparison of the basic concepts of fuzzy sets and crisp (common) sets as well as with the main references concerning the development of the theory and application of the fuzzy field of mathematics.

In the second chapter the theory of fuzzy sets in fully treated from the definition of fuzzy set to the integrating fuzzy functions over fuzzy domain – including the operations to and functions of fuzzy sets and fuzzy numbers, as well as fuzzy arithmetic. The third chapter deals with the fuzzified relationships and properties of fuzzy relations.

In the fourth chapter the linguistic variables and their applications are treated including fuzzy control and approximate reasoning and their applications. The fifth chapter deals with the measure theory in connection with fuzzy sets. Fuzzy measures for crisp and fuzzy sets including fuzzy integrals, probability concepts, applications and the measures of fuzziness are also introduced and discussed.

The sixth chapter’s topic is the fuzzy data analysis including the qualitative and quantitative ones, as well as fuzzy inference.

The book is closed by a full bibliography (more than 300 entries on 18 pages) and an index.

Reviewer: J.Tankó (Budapest)

### MSC:

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

03E72 | Theory of fuzzy sets, etc. |

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

28E10 | Fuzzy measure theory |