## Fuzzy Sets Theory and ApplicationsAndré Jones, Arnold Kaufmann, Hans-Jürgen Zimmermann Problems in decision making and in other areas such as pattern recogni tion, control, structural engineering etc. involve numerous aspects of uncertainty. Additional vagueness is introduced as models become more complex but not necessarily more meaningful by the added details. During the last two decades one has become more and more aware of the fact that not all this uncertainty is of stochastic (random) cha racter and that, therefore, it can not be modelled appropriately by probability theory. This becomes the more obvious the more we want to represent formally human knowledge. As far as uncertain data are concerned, we have neither instru ments nor reasoning at our disposal as well defined and unquestionable as those used in the probability theory. This almost infallible do main is the result of a tremendous work by the whole scientific world. But when measures are dubious, bad or no longer possible and when we really have to make use of the richness of human reasoning in its variety, then the theories dealing with the treatment of uncertainty, some quite new and other ones older, provide the required complement, and fill in the gap left in the field of knowledge representation. Nowadays, various theories are widely used: fuzzy sets, belief function, the convenient associations between probability and fuzzines~ etc ••• We are more and more in need of a wide range of instruments and theories to build models that are more and more adapted to the most complex systems. |

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### Contents

MATHEMATICS AND FUZZINESS | 3 |

RADONNIKODYM THEOREM FOR FUZZY SETVALUED MEASURES | 39 |

CONSTRUCTION OF A PROBABILITY DISTRIBUTION FROM A FUZZY INFORMATION | 51 |

CONVOLUTION OF FUZZYNESS AND PROBABILITY | 61 |

FUZZY SETS AND SUBOBJECTS | 69 |

From theory to applications | 77 |

Outline of a Theory of Usuality Based on Fuzzy Logic | 79 |

FUZZY SET THEORY AND MATHEMATICAL PROGRAMMING | 99 |

METHODOLOGY AND APPLICATIONS Elie Sanchez | 213 |

Various particular applications | 231 |

MULTI CRITERIA DECISION MAKING IN CRISP AND FUZZY ENVIRONMENTS | 233 |

FUZZY SUBSETS APPLICATIONS IN OR AND MANAGEMENT | 257 |

CHARACTER RECOGNITION BY MEANH OF FUZZY SET REASONING | 301 |

COMPUTERIZED ELECTROCARDIOGRAPH AND FUZZY SETS | 317 |

MEDICAL APPLICATIONS WITH FUZZY SETS | 331 |

FUZZY SUBSETS IN DIDACTIC PROCESSES | 349 |

### Other editions - View all

Fuzzy Sets Theory and Applications André Jones,Arnold Kaufmann,Hans-Jürgen Zimmermann Limited preview - 2012 |

Fuzzy Sets Theory and Applications André Jones,Arnold Kaufmann,Hans-Jürgen Zimmermann No preview available - 2011 |

### Common terms and phrases

algorithm alternative Anal analysis assume concept consider constraints corresponding crisp criteria decision defined definition degree denote determined dichotomic tree Dubois electrocardiography elements entropy evaluation example expert systems expressed figure finite fuzzy interval fuzzy logic fuzzy measure fuzzy number fuzzy random variable fuzzy set theory fuzzy subset given graph hybrid numbers interpretation Kaufmann knowledge knowledge representation L.A. Zadeh labelling file linear programming linguistic logic programming LOWEN Math mathematical programming matrix maximal maximum membership functions method morphism objective function obtain operator optimal pixels possibility distribution Prade probability distribution problem proof path properties proposition Radon-Nikodym theorem random fuzzy random variable representation represented rule Sanchez semantic set-valued measure Sets and Systems solution supp support pair theorem Theory and Applications tion topological spaces tree decompositions tuples unit interval usual value usuality-qualified vector voting Yager Zimmermann