对划分的一个粒度公式的研究

南京大学学报(自然科学版) ›› 2013, Vol. 49 ›› Issue (5): 546–552.

对划分的一个粒度公式的研究

林姿琼，姚华

出版日期:2014-01-21 发布日期:2014-01-21
作者简介:(福建省粒计算及其应用重点实验室,闽南师范大学漳州,363000)
基金资助:
国家自然科学基金面上项目（61170128），福建省自然科学基金（2012J01294），福建省教育厅科技项目（JA12222），福建省计算机应用技术和信号与信息系统研究生教育创新基地（闽高教[2008]114号）

Study of one granularity formula of partitions

L Zi-Qiong, Yao Hua

Online:2014-01-21 Published:2014-01-21
About author:(Laboratory of Granular Computing, Minnan Normal University, Zhangzhou, 363000, China)

摘要/Abstract

摘要： 对于划分的粒度，现在已经定义了很多公式。相对于同一个论域来说，这些定义所遵循的一个整体的原则显然是划分块数越少其粒度越大。对于同一论域的具有相同块数的两个不同划分，在某些情况下，其粒度也被认为是不同的，可称之为局部原则。现有的公式基本上都兼顾了这两个方面。讨论一个相对简单的公式，且主要研究的是局部原则对整体原则某种程度的破坏。首先定义划分的方差，给出划分的粒度公式与划分的方差之间的关系。然后给出一个界限，证明在相同论域上，当一个划分的块数大于另一个划分的块数超过这个界限时，这个划分的粒度一定大于另一个划分的粒度。

Abstract: Many formulae of granularity of partitions have been defined. For a same universe, these formulae follow a whole principle that the fewer the amount of partition blocks are, the larger the granularity of partitions are. In some cases, granularities of two different partitions on a same universe are considered different. We call this the part principle. The existing formulae fundamentally follow both the whole principle and the part principle. This paper discusses comparatively simple one of granularity formulae, and the destroying on the whole principle caused by the part principle is mainly focused on. First, we define the variance of partitions, and present the relationship between the granularity formula of partitions discussed in this paper and the variance of partitions. Then we give a limit, and prove that in the same universe, if the number of the blocks of a partition is bigger than that of the other partition beyond the limit, the granularity of this partition is certainly bigger than that of the other partition

林姿琼，姚华. 对划分的一个粒度公式的研究[J]. 南京大学学报(自然科学版), 2013, 49(5): 546–552.

L Zi-Qiong, Yao Hua. Study of one granularity formula of partitions[J]. Journal of Nanjing University(Natural Sciences), 2013, 49(5): 546–552.

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