数据挖掘意义下函数依赖及其变形的数学机理

The Mathematical Mechanism of Functional Dependency and Its Deformation in the View of Data Mining

为了解决长期以来经典函数依赖语义性解释不足且数学解释缺失的问题,本文从数据挖掘的角度研究了数据库函数依赖与其四种重要的变形。通常函数依赖的变形一般有知识依赖、关联规则、属性蕴含及决策规则,本文着重从以下三个角度进行研究,其一是从逻辑推理的角度探讨函数依赖与其变形对Armstrong公理系统的满足性,其二是从规则度量的角度分析函数依赖与其变形的度量,其三从语义角度出发总结函数依赖与其变形的关系。在此基础上,利用函数理论从等价类的角度建立了函数依赖的数学模型,对经典函数依赖及其变形做出了较好的解释。

The database functional dependency and its four important deformations were investigated from the perspective of data mining in order to solve the problem that the semantic interpretation of classical functional dependency is insufficient and the mathematical interpretation is missing for a long time.In general,these deformations of functional dependency have knowledge dependency,association rule,attribute implication and decision rule.The study was carried from following three aspects,the satisfiability to Armsrong axiom was researched from the view point of logic reasoning firstly,then the measurement of functional dependency and its deformations was analyzed from the view point of rule measurement secondly,and thirdly the relationship between database functional dependency and its deformations was summarized from the perspective of semantic.Based on the above researches,the unified mathematical model of functional dependency is established by using function theory from the Angle of equivalent class theory,and the classical functional dependency and its deformations is explained.