## A First Course in Fuzzy Logic, Third EditionThe second edition of the popular A First Course in Fuzzy Logic will continue to provide the ideal introduction to the theory and applications of fuzzy logic. The authors provide a firm mathematical basis for the calculus of fuzzy concepts-necessary to design intelligent systems-and give the student a solid background for further studies and real-world applications. This new edition provides many new exercises designed to enhance the reader's understanding of the concepts. The authors have expanded on the algebra background needed for the more advanced topics, and include significant new material on basic connectives and the algebraic properties of fuzzy logic, rough sets, conditional events, distributions of random sets, and derivatives of fuzzy measures. With its comprehensive updates, A First Course in Fuzzy Logic, Second Edition presents all the background necessary for students to begin using fuzzy logic in its many-and rapidly growing-applications. |

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### Contents

The Concept of Fuzziness | 1 |

Some Algebra of Fuzzy Sets | 19 |

Fuzzy Quantities | 47 |

Logical Aspects of Fuzzy Sets | 61 |

Basic Connectives | 83 |

Additional Topics on Connectives | 143 |

Fuzzy Relations | 177 |

Universal Approximation | 191 |

Possibility Theory | 207 |

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### Common terms and phrases

a-cuts antiautomorphism approximate Archimedean t-norm associated Aut(I Aut(l automorphism averaging operator belief function binary operation Boolean algebra Chapter comonotonic complete lattice compute conditional consider convex Corollary defined Definition denote dual element equation equivalence classes equivalence relation example Exercise formulas Frank system fuzzy concepts fuzzy control fuzzy equivalence relation fuzzy implication fuzzy integrals fuzzy logic fuzzy measure fuzzy numbers fuzzy partition fuzzy quantities fuzzy relation fuzzy sets fuzzy subset given implies interval isomorphism Kleene algebra L-generators Lebesgue mapping mathematical measurable space membership function metric space Mobius inversion Morgan algebra Morgan systems morphisms natural negation nilpotent t-norm nonnegative notation partially ordered set possibility distribution probability measure probability space Proof properties propositional calculus random set random variable respect rough sets rules satisfies set functions Show Stone algebra strict t-norm subgroup Suppose t-conorm Theorem three-valued truth values Verify