多标记粒度不完备信息系统的粗糙近似*

南京大学学报(自然科学版) ›› 2013, Vol. 49 ›› Issue (2): 250–257.

多标记粒度不完备信息系统的粗糙近似*

顾沈明**，叶晓敏，吴伟志

出版日期:2015-10-22 发布日期:2015-10-22
作者简介: (浙江海洋学院数理与信息学院，舟山 316000)
基金资助:
国家自然科学基金(61272021,61075120,11071284,61173181)，浙江省自然科学基金(LZ12F03002)，浙江省科技厅优先主题重大项日(2008C13068)

Rough set approximations in incomplete information systems
with multrlabeled granules

Gu Shen-Ming ,Ye Xiao-Min ,Wu Wei - Zhi

Online:2015-10-22 Published:2015-10-22
About author:(School of Mathematics,Physics and information Science,Zhejiang Ocean University,Zhoushan,316000,China)

摘要/Abstract

摘要： 在粒计算看来，一个粒是由多个比较小的颗粒组成更大的一个单元.在许多场合下，由于不同
尺度对数据集分割而得到不同层次的信息粒度，这些不同的信息粒度可以用不同的标记块来区分.首先
介绍了用一个满射来定义标记块的概念，接着在标记块的基础上给出了多标记粒度结构.针对多标记粒
度结构，先给出了完备信息系统中粒度信息变换函数，接着在多标记不完备信息系统中重新定义了粒度
信息变换函数.由粒度信息变换函数，可以在多标记不完备信息系统中得到信息粒度的一个层次结构.
在每一个层次中，利用非对称相似关系定义相似类，进而定义集合的上近似、下近似、近似精度和粗糙度
等概念.在不同层次之间，分别讨论了上近似、下近似、近似精度和粗糙度的性质，在不同的知识粒度下
探索的知识近似的变化规律.

Abstract: The key to granular computing is to make use of granules in problem solving. With the view point of
granular computing,the notion of a granule may be interpreted as one of the numerous small particles forming a lai-
ger unit.ln many situations, there arc different granules at different levels of scale in data sets having hierarchical
scale structures.The different granules can be described by different labeled blocks.The concept of labeled blocks de-
termined by a surjective function is first introduced in this paper. Based on the labeled blocks,the multi-labeled gran-
ular structure is also introduced.Then, the function of granular information transformation is proposed in multi-la-
bcled complete information systems. Duc to the rampant existence of incomplete information systems in practice, a
new approach for granular knowledge acquisition in incomplete information system became necessity.Therefore，a
new function of granular information transformation is defined in multi-labeled incomplete information systems. With
the function of granular information transformation,a hierarchical structure of granules can be obtained in multi-la-
beled incomplete information system. At every level，the similarity class can be defined by using asymmetric similarity
relation,and the lower and upper approximations of any subset of universe in multi-labeled incomplete information
systems can be defined based on similarity class. Analogously,accuracy of approximations and roughness are also de-
fined as usual at one level. Furthermore, the properties of lower approximations, upper approximations, accuracy of
approximations and roughness between different levels arc discussed respectivcly,and some examples arc also illus-
trativcd.Those properties may be useful to find laws of knowledge variation in multi-labeled incomplete information
system while the granular sizc changing.

顾沈明**，叶晓敏，吴伟志
. 多标记粒度不完备信息系统的粗糙近似*[J]. 南京大学学报(自然科学版), 2013, 49(2): 250–257.

Gu Shen-Ming ,Ye Xiao-Min ,Wu Wei - Zhi. Rough set approximations in incomplete information systems
with multrlabeled granules
[J]. Journal of Nanjing University(Natural Sciences), 2013, 49(2): 250–257.

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