基于模糊粗糙集的区间集决策表不确定性度量

Uncertainty measurement of interval set decision tables based on fuzzy rough set

模糊粗糙集融合了模糊集与粗糙集两者的优点,是一种更优的不确定性数据处理模型,但将其应用于区间集决策表的研究较为罕见。本文针对区间集决策表,引入模糊粗糙集模型,并在该模型上定义了模糊近似粗糙度等概念;模糊近似粗糙度仅能刻画近似分类的不确定性,为了达到更加全面的度量效果,接着在模糊粗糙集模型中提出模糊粒结构,并基于该结构定义模糊条件熵,模糊条件熵仅能刻画粒化结构的不确定性;最后,将两种度量进行信息融合,提出一种混合不确定性度量,并获得粒化单调性等性质。实例表明,文中给出的度量对研究区间集决策表的不确定性具有指导作用。

Fuzzy rough set combines the advantages of both fuzzy set and rough set.It is a better model for processing uncertain data,but it is rare to be applied on interval set decision tables.In this paper,aimed at interval set decision tables,a fuzzy rough set model is introduced,and concepts such as fuzzy approximate roughness are defined on this model.Fuzzy approximate roughness can only describe the uncertainty of approximate classification.In order to achieve a more comprehensive measurement effect,then a fuzzy grain structure is proposed in the fuzzy rough set model,and fuzzy conditional entropy is defined based on this structure.Fuzzy conditional entropy can only describe the uncertainty of the structural structure.Finally,to fuse the information of the two metrics,a mixed uncertainty metric is proposed,and properties such as granular monotonicity are obtained.The example shows that the measurement given in the article has a guiding effect on the uncertainty of the research interval set decision tables.