## Future Directions of Fuzzy Theory and SystemsThis monograph includes expanded selected papers presented in the “Workshop on the Future Directions of Fuzzy Theory and Systems”. It contains many recent developments in the field and provides valuable insights into the future direction and applications of fuzzy theory and systems. |

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### Contents

Toward Intelligent Computing | 10 |

Mathematical Foundation and Engineering Application | 40 |

Chapter 5 | 57 |

Chapter 6 | 70 |

Chapter 7 | 88 |

Chapter 8 | 107 |

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### Common terms and phrases

additive fuzzy system analysis antecedent membership functions applications approach Axiomatic Set Theory calculus cartesian products centroid chapter classical mathematics constraints conversion procedure crisp data pairs database decomposable approximation defined defuzzification ellipsoid Ellipsoidal Learning equation error example expert systems FCPN3 function approximation fuzzy clustering fuzzy counterpropagation network fuzzy expert system fuzzy function approximation fuzzy graphs fuzzy inference fuzzy logic fuzzy number fuzzy rules fuzzy sets fuzzy subsets fuzzy system hence hidden units hybrid IEEE if-then rules inference conclusion input linguistic terms input vector input-output interpolation K.S. Leung knowledge Kosko L.A. Zadeh learning algorithms Lyapunov function matrix membership functions membership grades method multiple-valued logic natural language Nature Journal Neural Networks nonlinear operators output P.Z. Wang parameters pattern polynomial rules problem query real number representation rule base space subsystem inference supervised learning System of Medium Theorem truth value unsupervised weight vectors Wujia Zhu Xi'an Xi'an Xiao