## Computing with Words in Information/Intelligent Systems 1: FoundationsThese two volumes consIstmg of Foundations and Applications provide the current status of theoretical and empirical developments in "computing with words". In philosophy, the twentieth century is said to be the century of language. This is mainly due to Wittgenstein who said: "The meaning of a word is its use in the language game". "The concept game is a concept with blurred edges". In the first phrase, "the language game" implies the everyday human activity with language, and in the latter, "game" simply implies an ordinary word. Thus, Wittgenstein precisely stated that a word is fuzzy in real life. Unfortunately this idea about a word was not accepted in the conventional science. We had to wait for Zadeh's fuzzy sets theory. Remembering Wittgenstein's statement, we should consider, on the one hand, the concept of "computing with words" from a philosophical point of view. It deeply relates to the everyday use of a word in which the meaning of a word is fuzzy in its nature. |

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### Contents

Fuzzy Logic Computing with Words | 3 |

PERFORMING APPROXIMATE REASONING WITH WORDS? | 24 |

Approximate Reasoning as a Basis for Computing with Words | 50 |

What is Intelligent Measurement? | 78 |

Semiotics and Computational Linguistics On Semiotic Cognitive Information Processing | 93 |

Analogies and Contexts | 119 |

Problems of Interpretation in the Social Sciences | 136 |

A TERMINOLOGICAL PRIMER | 154 |

Fuzzy Negation | 297 |

TRIANGULAR OPERATIONS NEGATIONS AND SCALAR CARDINALITY OF A FUZZY SET | 326 |

FUZZY IMPLICATIONS IN APPROXIMATE REASONING | 342 |

On the Semantics of Fuzzy Linguistic Quantifiers | 358 |

Evaluating Linguistic Expressions and Functional Fuzzy Theories in Fuzzy Logic | 383 |

Calculation over Verbal Quantities | 409 |

Aggregation of Linguistic Information Based on a Symbolic Approach | 428 |

A Computational Framework to Compute with Words | 443 |

Fuzzy Logic and Rough Sets | 183 |

Towards an Adaptive Calculus of Granules | 201 |

Semantics and Modelling of Flexible Time Indications | 229 |

Towards Fuzzy Logic | 259 |

Study on a Framework for Solving Illdefined Problem Using Patterns and Symbols | 479 |

GroupTheoretic Approach to Computing with Words in InformationIntelligent Systems | 495 |

### Common terms and phrases

algebra algorithm Applications approach approximate reasoning Artificial Intelligence axioms basic binary binary relation Cartesian product complement computational semiotics computing with words concept consider corresponding crisp decision defined Definition defuzzification denote domain Dubois elements example expressions finite formal formula fuzzy implication fuzzy logic fuzzy quantities fuzzy relation fuzzy set theory Fuzzy Systems granularity granulation IEEE imprecise inference input Intelligent International interpretation knowledge labels linguistic LTI's mapping mathematical measurement membership functions mereology meta-object natural language negation neighborhood system notion object network operations output pattern possibilistic possibilistic logic possible Prade predicate probability problem processing properties proposition quantifier real numbers representation represented rough set rough set theory rules scalar cardinalities semantic semiotic Sets and Systems structure t-conorm t-norm T. Y. Lin Theorem tuple uncertainty vague variable vector verbal quantities virtual meanings Yager Zadeh