## Fuzzy Set Theory and Advanced Mathematical ApplicationsFuzzy Set Theory and Advanced Mathematical Applications contains contributions by many of the leading experts in the field, including coverage of the mathematical foundations of the theory, decision making and systems science, and recent developments in fuzzy neural control. The book supplies a readable, practical toolkit with a clear introduction to fuzzy set theory and its evolution in mathematics and new results on foundations of fuzzy set theory, decision making and systems science, and fuzzy control and neural systems. Each chapter is self-contained, providing up-to-date coverage of its subject. Audience: An important reference work for university students, and researchers and engineers working in both industrial and academic settings. |

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### Contents

ON THE EVOLUTION OF THE MATHEMATICS | 3 |

CLOSEDNESS AND UPPER SEMICONTINUITY | 35 |

AN ORDERTHEORETHIC APPROACH | 67 |

Copyright | |

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### Common terms and phrases

aggregation rule algorithm ample field applications approach approximation arbitrary Baets binary Cappelle characterized classical closed-valued closedness complete lattice component computing consider Cooman crisp defined definition defuzzification denoted dom(F E.E. Kerre elements example false FMMs following properties hold fuzzy control fuzzy logic fuzzy multivalued mappings fuzzy numbers fuzzy preference fuzzy relational fuzzy set theory fuzzy singleton Fuzzy Systems fuzzy topological spaces fuzzy variable hence hierarchical aggregation implication operator input intersection Kacprzyk Lagrange interpolant left-continuous linear Lagrange interpolant linguistic mathematical membership functions method neural networks neuro-fuzzy neuron non-void normalized notion OWA operators parameters partial mappings possibilistic truth value possibilistic variable possibility measure preference relation problem Proof proposition variable propositional logic reliability theory resp root system rule base satisfies the condition Sets and Systems structure function subset surjective t-norm Theorem tion triangular norm uncertainty universe X upper semi-continuity W3-transitive xaPp Zadeh