不完备多粒度序信息系统的粗糙近似

南京大学学报(自然科学版) ›› 2015, Vol. 51 ›› Issue (2): 361–367.

不完备多粒度序信息系统的粗糙近似

戴志聪，吴伟志*

出版日期:2015-03-06 发布日期:2015-03-06
作者简介: (浙江海洋学院数理与信息学院舟山316022)
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重点项目(LZ12F03002)

Rough approximations in incomplete multi-granular ordered information systems

Dai Zhicong, Wu Weizhi*

Online:2015-03-06 Published:2015-03-06
About author:(School of Mathematics, Physics and Information Science, Zhejiang Ocean University,Zhoushan, 316022, China)

摘要/Abstract

摘要： 粒计算是知识表示和数据挖掘的一个重要方法. 它模拟人类思考模式，以粒为基本计算单位，以处理大规模复杂数据和信息等建立有效的计算模型为目标. 针对具有多粒度标记的不完备序信息系统的知识获取问题，首先，介绍了不完备多粒度序信息系统的概念，并在不完备多粒度序信息系统中定义了优势关系，同时给出了由优势关系导出的优势类，并进一步定义了基于优势关系的集合的序下近似与序上近似的概念，并讨论了它们性质.

Abstract: An important task of knowledge discovery is to establish relations among granules such as classes, clusters, sets, groups, concepts, etc. Granular computing (GrC) is a basic issue in knowledge representation and data mining. It imitates human being’s thinking and its objective is to establish effective computation models and to seek for an approximation scheme for dealing with large scale complex data and information. A granule is a primitive notion in GrC which is a clump of objects (points) drawn together by the criteria of indistinguishability, similarity or functionality. It may be interpreted as one of the numerous small particles forming a larger unit. The set of granules provides a representation of the unit with respect to a particular level of granularity. The information granulation is a process of constructing information granules, which granulates a universe of discourse into a family of disjoint or overlapping granules. Rough set theory is one of the most advanced approaches that popularize GrC. Most applications based on rough set theory belong to the attribute-value representation model, i.e. information systems. The Pawlak’s rough set model is mainly concerned with the approximation of sets described by a single binary relation on the universe of discourse. Due to the rampant existence of multi-granular information systems with missing values and ordered attributes, the purpose of this study is to discuss representation of information granules and rough approximations of concepts in incomplete multi-granular ordered information systems. The concept of incomplete multi-granular ordered information systems is first introduced. In an incomplete multi-granular ordered information system, data with missing values are represented by different scales at different levels of granulations having a granular information transformation from a finer to a coarser ordered attribute domain.
Dominance relations on the universe of discourse from an incomplete multi-granular ordered information system are then defined. Dominated labeled classes determined by dominance relations are further constructed. Finally, ordered lower and ordered upper approximations based on dominance relations are explored. Properties of approximations with different levels of granulations are further examined.

戴志聪，吴伟志*. 不完备多粒度序信息系统的粗糙近似

[J]. 南京大学学报(自然科学版), 2015, 51(2): 361–367.

Dai Zhicong, Wu Weizhi*
. Rough approximations in incomplete multi-granular ordered information systems

[J]. Journal of Nanjing University(Natural Sciences), 2015, 51(2): 361–367.

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