区间集概率粗糙集的单调性

The Monotonicity of Interval-set Probabilistic Rough Sets

概率粗糙集利用条件概率和两个阈值给出被近似集合和等价类之间满足一定包含程度的近似刻画。区间集通过上、下界给出了一个概念的外延范围。本文将被近似集合推广到区间集,提出了刻画概念外延范围的区间集概率粗糙集,研究了它们的性质。讨论了当被近似的区间集发生变化时,区间集概率粗糙下、上近似的单调性;进一步研究了当两个阈值单调时,相应的区间集概率粗糙下、上近似的单调性。

Applying conditional probability and two thresholds, the probabilistic rough set is intro- duced to depict the approximation characterizations of the inclusion degree between the approximated set and the equivalence classes. While interval set shows the range of the extension for some concept by using a pair of the upper and lower bounds. In this paper, the approximated set is extended to an interval set, and the interval set probabilistic rough set {or the range of the extension of some concept is then proposed. Related properties of them are discussed. The interval set probabilistic rough lower and upper approximations are monotone when the approximated interval set changed. Furthermore, the monotonicity of the corresponding interval set probabilistic rough lower and upper approximations is also investigated when the two thresholds are monotone.