具有等级的数据的属性相似性
Attribute Dependencies for Data with Grades
摘要：
本文研究了涉及等级的数据中的属性依赖关系，例如对象为红色的等级或两个对象相似的等级。因此，我们扩展了经典的议程，允许分级，或模糊，属性，而不是布尔属性的情况下，属性的影响，并允许近似匹配的相似程度的基础上，而不是精确匹配的情况下，功能依赖。从某种意义上说，我们从现在可用的依赖性理论中固有的二价转向了一个更灵活的涉及等级的设置。这种转变具有深远的影响。我们认为，一个合理的理论的依赖关系，可以开发利用数学模糊逻辑。也就是说，依赖关系理论是基于一个坚实的逻辑演算，就像经典依赖关系是基于经典逻辑一样。例如，我们不是以特定的方式处理相似度，而是始终将它们视为真值，就像经典理论中处理真（匹配）和假（不匹配）一样。此外，几个概念直观地拥抱在等级的存在，如一个特定的依赖或程度的蕴涵的有效性程度，自然出现，并在所提出的方法中得到概念上干净的处理。在本文中，我们讨论了动机，提供了基本的语法和语义概念，并开发了基本的结果，其中包括蕴涵的依赖，相关的封闭结构，逻辑的依赖与两个版本的完整性定理，结果和算法，完全非冗余集的依赖，关系和一个可能的约简接口的经典依赖，以及与具有相似性的域上的函数依赖性的关系。
英文摘要：
This paper examines attribute dependencies in data that involve grades, such as a grade to which an object is red or a grade to which two objects are similar. We thus extend the classical agenda by allowing graded, or fuzzy, attributes instead of Boolean attributes in case of attribute implications, and allowing approximate match based on degrees of similarity instead of exact match in case of functional dependencies. In a sense, we move from bivalence, inherently present in the now-available theories of dependencies, to a more flexible setting that involves grades. Such a shift has far-reaching consequences. We argue that a reasonable theory of dependencies may be developed by making use of mathematical fuzzy logic. Namely, the theory of dependencies is then based on a solid logic calculus the same way the classical dependencies are based on classical logic. For instance, rather than handling degrees of similarity in an ad hoc manner, we consistently treat them as truth values, the same way as true (match) and false (mismatch) are treated in classical theories. In addition, several notions intuitively embraced in the presence of grades, such as a degree of validity of a particular dependence or a degree of entailment, naturally emerge and receive a conceptually clean treatment in the presented approach. In the paper, we discuss motivations, provide basic notions of syntax and semantics, and develop basic results which include entailment of dependencies, associated closure structures, a logic of dependencies with two versions of completeness theorem, results and algorithms regarding complete non-redundant sets of dependencies, relationship to and a possible reductionist interface to classical dependencies, and relationship to functional dependencies over domains with similarity.
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