## Fuzzy sets and fuzzy logic: the foundations of application--from a mathematical point of view |

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### Contents

Logical Preliminaries | 1 |

Basic fuzzy set theory | 37 |

Set equations with fuzzy sets | 97 |

Copyright | |

4 other sections not shown

### Common terms and phrases

additionally approximate solutions binary cartesian product connectives consider continuous t-norm Corollary crisp data set defined discussed disjunction evaluation finite Furthermore fuzzified fuzzy controller fuzzy data fuzzy equations fuzzy equivalence relation fuzzy measure fuzzy model fuzzy partial ordering fuzzy relational equations fuzzy set theory Fuzzy Sets Syst fuzzy subsets given global Gottwald hence holds true idempotent IF(X implication inequality irreflexive left continuous linguistic logically valid lower semicontinuous many-valued logic membership degrees membership function monotonicity negation function notation numbers obviously operator output space Pedrycz problem Proof property LSC(t proposition 1.19 prove quantifiers respect rule of inference solvability degree subset property sufficient condition suitable superset property supp Suppose system of fuzzy t-conorms t-transitive theorem threshold level tion Transt(R truth degree truth functions universe of discourse usual values well-formed formula yeBi Zadeh zero divisors