## A first course in fuzzy logic"Classical and Fuzzy Concepts in Mathematical Logic and Applications" explains how to use the English language with logical responsibility, how to define and use formal language, and how to reason correctly. Specific issues examined include a discussion of propositional and predicate logic, logic networks. logic programming, proof of correctness, semantics, syntax, and theorems of Herbrand and Kalman. The text emphasizes the use of logic in computer science, addresses questions in automatic deduction, and introduces a systematic parallel between aspects of classical logic and fuzzy mathematical logic. |

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### Contents

The Concept of Fuzziness | 1 |

Some Algebra of Fuzzy Sets | 17 |

Fuzzy Quantities | 37 |

Copyright | |

12 other sections not shown

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### Common terms and phrases

a-cuts additive approximate Archimedean t-norm automorphism belief function binary operation Boolean algebra Chapter comonotonic complete lattice conditional conorms consider convex cr-field defined definition defuzzification DeMorgan algebra denote elements equivalence classes equivalence relation example Exercise finite set formulas function F fuzzy concepts fuzzy control fuzzy implication fuzzy integrals fuzzy logic fuzzy measure fuzzy numbers fuzzy quantities fuzzy relation fuzzy sets fuzzy subset implies imprecise indicator function induces interval isomorphism knowledge Lebesgue integral logical connectives logically equivalent mathematical measurable space membership functions metric space Mobius inversion modeling monotone of order nilpotent nilpotent t-norm nonnegative notation partially ordered set polynomials possibility distribution possibility measure probabilistic probability density probability measure probability space problem Proof properties propositional calculus random set random variable real numbers respect rules satisfying set functions Show simple functions specify Suppose t-conorm t-norm Theorem theory three-valued truth values two-valued Verify