形式背景上近似推理生成决策蕴涵研究

Study on the Approximate Reasoning Models of Decision Implication in Formal Decision Context

基于形式背景获取决策蕴涵、概念规则等知识是数据分析、机器学习的重要研究内容之一.首先,利用属性逻辑语义对决策蕴涵的特性进行刻画.其次,在经典二值逻辑框架下分析决策蕴涵、概念规则的基于全蕴涵三I推理思想及分离规则(Modus ponens,MP)和逆分离规则(Modus tonens,MT)的近似推理模式的特征,证明决策蕴涵的MP、MT近似推理结论是决策蕴涵,概念规则的MP、MT近似推理结论是概念规则等结论.引进属性逻辑公式的伪距离,在属性逻辑伪距离空间中分析推理对象范围参数变化对决策蕴涵MP、MT近似推理结论的影响.最后,提出若干通过MP、MT近似推理生成决策蕴涵、概念规则及拟决策蕴涵的模式和方法,数值实验验证了所提方法的有效性.

It is one of the contents of data analysis and machine learning to obtain the knowledge of decision implication and conceptual rule from formal decision context.Firstly,attribute logic semantics is used to analyze the characteristics of decision implication.Secondly,in the classical binary logic framework,the characteristics of modus ponens(MP)and modus tonens(MT)approximate reasoning models based on the all implication three-I inference idea is analyzed.It is proved that the MP and MT approximate reasoning conclusions of decision implications are decisions implications,the MP and MT approximate reasoning conclusions of concept rules are concept rules.The pseudo-metric of attribute logic formula is introduced,and the influence of MP and MT approximate reasoning conclusions of decision implication as the reasoning object range parameter changes in attribute logic pseudometric space is analyzed.Finally,some models and methods of generating decision implication,concept rules and quasi-decision implication through MP and MT approximate reasoning based on existing decision implication,concept rules and quasi-decision implication are proposed,numerical experiments show that the proposed methods are effective.