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不确定性度量是粗糙集理论中的关键问题之一.对于覆盖粗糙模糊集的不确定性度量,虽然人们已经提出一些度量方法,但这些度量方法都存在一定局限性.首先,分析了已有两种度量方法,发现其中一种度量方法需要人工设定参数,其度量结果带有主观性;另一种度量方法当下近似为空时与上近似无关,不符合人们的直观认识.然后,从不确定性的物理含义出发,将上、下近似看成是多维空间中的点,并以它们间的距离作为不确定性的度量.最后,对这种新的度量方法的性质进行了分析.结果表明该方法克服了已有度量方法的局限性,从定量的角度为刻画覆盖粗糙模糊集的不确定性提供了方法.
Uncertainty measure is one of the key problems in rough set theory.For the uncertainty measure covering rough fuzzy set, although some measure methods have been proposed, these measure methods have some limitations.First, Two kinds of measurement methods found that one of the measurement methods need to manually set parameters, the measurement results with subjectivity; the other measurement method is empty when the moment is not related with the upper approximation, does not meet the people’s intuitive understanding.Then, from The physical meaning of uncertainty, the upper and lower approximation as a point in multi-dimensional space, and the distance between them as a measure of uncertainty.Finally, the nature of this new measurement method is analyzed. The results show that this method overcomes the limitations of the existing measurement methods and provides a quantitative approach to describe the uncertainty of the coverage of the rough fuzzy sets.