决策形式背景的两种不确定性度量  

Two Measures of Uncertainty in Decision Formal Contexts

作　　者：李仲玲[1] 米据生[2] 刘晓娟[2] 

机构地区：[1]河北师范大学汇华学院,河北石家庄050091 [2]河北师范大学数学与信息科学学院,河北石家庄050024

出　　处：《模糊系统与数学》2015年第4期153-157,共5页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61170107);河北省教育厅基金资助项目(QN2014165)

摘　　要：定义形式背景中对象集合的一种粒覆盖,并给出其性质,由此得到粒上下近似概念。构造一种隶属度,并研究怎样度量一个决策形式背景的协调度,怎样度量形式背景和决策形式背景中粒粗糙集及粒粗糙类的模糊度。证明协调决策形式背景的协调度为1,可定义集的模糊度为零的结论,验证两种不确定性度量构造的合理性。这些结果将有助于进一步理解形式背景及决策形式背景的不确定理论。In this paper, a kind of covering called granular covering is first defined, and the properties of granular covering are discussed. In addition, the granular lower and upper approximations are introduced. Based on these concepts, a membership function is constructed. Next we focus on how to measure the consistency of a decision formal context and the fuzziness of a granular rough set and a granular rough classification in formal contexts and decision formal contexts. It is proved that the rationality of the measure by proving the consistency degree of a consistent decision formal context is one and the fuzziness measure of a definable decision equals to zero. The results can help us for understanding the uncertainty in formal contexts and decision formal contexts.

关 键 词：决策形式背景 粒覆盖 相似度 模糊度 

分 类 号：O159[理学—数学]