## An Introduction to Fuzzy Sets: Analysis and Design"The Pedrycz and Gomide text is superb in all respects. Its exposition of fuzzy-neural networks and fuzzy-genetic systems adds much to its value as a textbook" -- Lotfi A. Zadeh, University of California, Berkeley. The concept of fuzzy sets is one of the most fundamental and influential tools in computational intelligence. Fuzzy sets can provide solutions to a broad range of problems of control, pattern classification, reasoning, planning, and computer vision. This book bridges the gap that has developed between theory and practice. The authors explain what fuzzy sets are, why they work, when they should be used (and when they shouldn't), and how to design systems using them. The authors take an unusual top-down approach to the design of detailed algorithms. They begin with illustrative examples, explain the fundamental theory and design methodologies, and then present more advanced case studies dealing with practical tasks. While they use mathematics to introduce concepts, they ground them in examples of real-world problems that can be solved through fuzzy set technology. The only mathematics prerequisites are a basic knowledge of introductory calculus and linear algebra. |

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### Contents

Basic Notions and Concepts of Fuzzy Sets | 3 |

Fuzzy Set Operations | 31 |

InformationBased Characterization of Fuzzy Sets | 59 |

Terms of the Codebook | 74 |

Equations | 103 |

References | 126 |

References | 150 |

Fuzzy Sets and Probability | 151 |

Fuzzy Measures and Fuzzy Integrals | 205 |

RuleBased Computations | 221 |

Fuzzy Neurocomputation | 265 |

Fuzzy Evolutionary Computation | 303 |

Fuzzy Modeling | 327 |

Methodology | 361 |

Case Studies | 399 |

463 | |

### Common terms and phrases

a-cuts aggregation applications approximation associated Assume basic Cartesian product chapter chromosome clustering composition operator computing concept connections Consider constraints corresponding decision decoding defuzzification denote derive determine discussed elements encoding entropy evolution strategies example expression fuzzy controller fuzzy integral fuzzy logic fuzzy measure fuzzy model fuzzy neural network fuzzy relation fuzzy rules fuzzy systems fuzzy truth values fuzzy-relational equations genetic algorithms inference instance interpretation intersection inverse inverse problem involves linear linguistic labels linguistic terms linguistic variable meaning measure of fuzziness membership function membership values method module neuron nodes nonlinear optimization problem output parameters Pedrycz performance probabilistic probability processing properties propositions quantified queue represented respectively rule-based scheme semantics sensors set theory Sets and Systems shown in figure solution specific structure sup-t t-norm temperature tion triangular norms truth qualification truth value uncertainty unit interval universe of discourse universe X vector vehicles Yager Zadeh