多粒度邻域粗糙模糊集及其不确定性度量

邻域粗糙集是经典粗糙集的一个扩展模型，研究其不确定性度量模型具有重要意义。在邻域粗糙集理论中，当前不确定性度量方面的研究工作主要专注于度量知识空间的粒度大小或边界域尺寸。在邻域系统中，对于目标概念为模糊时的情形，其不确定性不仅来自于邻域粒的边界域，还来自于正域和负域，当前的不确定性度量方法较少考虑这种情形。为此，构建了邻域粗糙模糊集模型，从粒计算的角度出发，进一步提出了多粒度邻域粗糙模糊集模型；针对多粒度邻域粗糙模糊集具有乐观性与悲观性的特点，借鉴Vague集中支持度和反对度的思想，设计了基于模糊度的多粒度模糊熵的不确定性度量方法，不仅符合人类的认知习惯，而且可以有效刻画整个邻域知识空间的结构信息。

Neighborhood-based multi-granulation rough fuzzy sets and their uncertainty measure

Neighborhood rough sets (NRS) model is an extension of classical rough sets. The research on the uncertainty measure of NRS is very important. In neighborhood rough sets, the current research on uncertainty measure mainly focuses on measuring the granularity or boundary size of knowledge space. However, when the target set is fuzzy, the uncertainty not only comes from boundary region, but also from the positive region and negative region, while the current methods do not consider this case. Firstly, the neighborhood-based rough fuzzy sets (NRFS) are proposed in this paper, from the perspective of granular computing, multi-granulation neighborhood-based rough fuzzy sets (NMGRFS) are further proposed. Moreover, based on the idea of support degree and object degree in vague sets, for the optimistic and pessimistic of NMGRFS, a fuzziness-based multi-granulation fuzzy entropy is established, which is not only in line with human cognitive habits, but also can effectively characterize the structural information of neighborhood knowledge space.