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The set of fuzzy rational numbers and flexible querying

机译：模糊有理数集和灵活查询

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摘要

A fuzzy bag is a bag in which each occurrence of an element is associated with a grade of membership. This notion can be viewed as a generalization of the concepts of set, fuzzy set and bag. The set of fuzzy integers (N_f) provides a general characterization in which all these different concepts are treated in a uniform way and can then be composed. In the field of databases, the use of fuzzy bags is motivated by their ability to manage both quantities and preferences. However, N_f becomes too restricted a framework when dealing with queries based on difference or division operations. So, a more general structure based on the set of fuzzy relative integers (Z_f) in which exact differences can be performed, has been first developed. In this paper, we carry on with this approach and we extend Z_f to the set of fuzzy rational numbers (Q_f). This context leads to define a closed system of multiplicative operations and allows to perform exact divisions. Applied to flexible querying of databases, Q_f and the notion of division on fuzzy numbers allow to generalize the relational division. They define a sound basis for queries involving ratios between quantities.
机译：模糊袋是其中元素的每次出现都与隶属度相关联的袋。这个概念可以看作是集合，模糊集合和袋的概念的概括。模糊整数（N_f）集合提供了一般特征，其中所有这些不同概念都以统一的方式处理，然后可以组成。在数据库领域，模糊袋的使用受其管理数量和偏好的能力的推动。但是，在处理基于差异或除法运算的查询时，N_f变得过于受限。因此，首先开发了一种基于模糊相对整数（Z_f）的更通用的结构，其中可以执行精确的差值。在本文中，我们继续使用这种方法，并将Z_f扩展到模糊有理数（Q_f）的集合。该上下文导致定义一个封闭的乘法运算系统，并允许执行精确的除法。通过将Q_f和模糊数除法的概念应用于数据库的灵活查询，可以概括关系除法。它们为涉及数量比率的查询定义了良好的基础。

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