多标记粒度不完备信息系统的粗糙近似  

Rough set approximations in incomplete information systems with multi-labeled granules

作　　者：顾沈明[1] 叶晓敏[1] 吴伟志[1] 

机构地区：[1]浙江海洋学院数理与信息学院,舟山316000

出　　处：《南京大学学报（自然科学版）》2013年第2期250-257,共8页Journal of Nanjing University（Natural Science）

基　　金：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目(2008C13068)

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.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 larger unit.In many situations,there are 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 determined by a surjective function is first introduced in this paper.Based on the labeled blocks,the multi-labeled granular structure is also introduced.Then,the function of granular information transformation is proposed in multi-labeled complete information systems.Due 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-labeled 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 defined as usual at one level.Furthermore,the properties of lower approximations,upper approximations,accuracy of approximations and roughness between different levels are discussed respectively,and some examples are also illustratived.Those properties may be useful to find laws of knowledge variation in multi-labeled incomplete information system while the granular size changing.

关 键 词：粒计算 不完备信息系统 多标记 粗糙集 非对称相似关系 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]