*(English)*Zbl 1009.03002

This is a slightly expanded version of the first edition (1998; Zbl 0956.03046), and again it is a nice and valuable presentation of seriously “fuzzified” tools of standard applied mathematics.

Chapters 1 to 4 remained unchanged. The other two chapters have been slightly modified and extended. In Chapter 5 on “Fuzzy geometry” the authors now also present results (of A. Rosenfeld and co-workers) from the late 1980s on degrees of adjacency and surroundness, on image enhancement and thresholding via fuzzy compactness, and on Hausdorff distances between fuzzy sets. In Chapter 6 on “Fuzzy abstract algebra” recent results (mainly of the first named author) are added on (local) solutions of nonlinear systems of fuzzy intersection equations of fuzzy singletons.

##### MSC:

03-01 | Textbooks (mathematical logic) |

03E72 | Fuzzy set theory |

00A06 | Mathematics for non-mathematicians |

00A05 | General mathematics |

00-01 | Textbooks (general mathematics) |

68U05 | Computer graphics; computational geometry |

68R99 | Discrete mathematics in relation to computer science |

54-01 | Textbooks (general topology) |

68-01 | Textbooks (computer science) |

54A40 | Fuzzy topology |

08A72 | Fuzzy algebraic structures |