决策形式背景的两种不确定性度量

Two Measures of Uncertainty in Decision Formal Contexts

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.