## Fuzzy Sets, Fuzzy Logic, ApplicationsFuzzy sets and fuzzy logic are powerful mathematical tools for modeling and controlling uncertain systems in industry, humanity, and nature; they are facilitators for approximate reasoning in decision making in the absence of complete and precise information. Their role is significant when applied to complex phenomena not easily described by traditional mathematics.The unique feature of the book is twofold: 1) It is the first introductory course (with examples and exercises) which brings in a systematic way fuzzy sets and fuzzy logic into the educational university and college system. 2) It is designed to serve as a basic text for introducing engineers and scientists from various fields to the theory of fuzzy sets and fuzzy logic, thus enabling them to initiate projects and make applications. |

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### Contents

MultiLevel Interval Numbers | 15 |

Fuzzy Numbers | 29 |

Arithmetic with Fuzzy Numbers | 69 |

Classical Sets | 95 |

Fuzzy Sets | 113 |

Fuzzy Relations | 141 |

Classical and ManyValued Logic | 159 |

Fuzzy Logic | 177 |

Decision Making and Applications | 209 |

Fuzzy Logic Control and Applications | 229 |

Answers Hints Solutions to Selected Exercises | 261 |

271 | |

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### Common terms and phrases

2-level intervals a-cuts a-level approximate reasoning arithmetic operations belong budget Cartesian product Chapter characteristic function classical logic classical sets compositional rule compound proposition Compute Consider the fuzzy control outputs correspondingly crisp decision Table defined defuzzification degree of membership Delphi method denoted Describe real numbers domain Draw the graph elements endpoints Exercise expressed FA(x fast car fia(x flat segment formula fuzzy logic fuzzy relation fuzzy set given HA(x hence intersection interval numbers intervals Aa inverse inverted pendulum level of presumption linguistic variable many-valued logic membership function modus ponens ordered pairs parasite population piecewise-quadratic fuzzy number point interval predicates real numbers close relation 1Z rule of inference Section selected set of p(x set theory sets and fuzzy shown in Fig subintervals subset supporting interval tion trapezoidal fuzzy number triangular fuzzy numbers true Truth set truth table truth value universal set Zadeh