## Modelling and Reasoning with Vague ConceptsVague concepts are intrinsic to human communication. Somehow it would seems that vagueness is central to the flexibility and robustness of natural l- guage descriptions. If we were to insist on precise concept definitions then we would be able to assert very little with any degree of confidence. In many cases our perceptions simply do not provide sufficient information to allow us to verify that a set of formal conditions are met. Our decision to describe an individual as 'tall' is not generally based on any kind of accurate measurement of their height. Indeed it is part of the power of human concepts that they do not require us to make such fine judgements. They are robust to the imprecision of our perceptions, while still allowing us to convey useful, and sometimes vital, information. The study of vagueness in Artificial Intelligence (AI) is therefore motivated by the desire to incorporate this robustness and flexibility into int- ligent computer systems. This goal, however, requires a formal model of vague concepts that will allow us to quantify and manipulate the uncertainty resulting from their use as a means of passing information between autonomous agents. I first became interested in these issues while working with Jim Baldwin to develop a theory of the probability of fuzzy events based on mass assi- ments. |

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### Contents

V | 1 |

VI | 9 |

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VIII | 15 |

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X | 19 |

XI | 22 |

XII | 24 |

XXXVI | 114 |

XXXVII | 120 |

XXXIX | 127 |

XL | 130 |

XLI | 139 |

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XIV | 29 |

XV | 36 |

XVI | 41 |

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XXI | 49 |

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XXIV | 69 |

XXV | 71 |

XXVI | 76 |

XXVII | 79 |

XXVIII | 85 |

XXIX | 86 |

XXX | 87 |

XXXI | 94 |

XXXII | 103 |

XXXIII | 105 |

XXXIV | 108 |

XXXV | 112 |

### Common terms and phrases

accuracy algorithm appropriate labels Archimedean t-conorm assertion assignment on labels assumption attribute groupings background knowledge Bayes Bayes theorem Bayesian branches chapter conditional distribution conditional probability conjunction consistent consonant msf constraint context corresponds coverage function curse of dimensionality database decision tree defined deﬁnition density described evaluate example focal sets follows fuzzy set theory fuzzy valuation generalised appropriateness measure given in definition Hence idempotence identify independent mass relation interpretation knowledge base label expressions label sets LID3 linguistic logical low2 mass assignment mass selection function medium membership functions merging merging algorithm mx(T operational semantics possibilistic possibility distribution prior distribution probability distribution proposed prototypes quantify random set satisfy Scatter plot set of appropriate set of labels shown in figure subset sunspot suppose t-norm tall theorem truth-functional truth-functionality uncertain knowledge uncertainty underlying vague concepts values Zadeh