• 中国计算机学会会刊
  • 中国科技核心期刊
  • 中文核心期刊

计算机工程与科学 ›› 2020, Vol. 42 ›› Issue (08): 1463-1471.

• 人工智能与数据挖掘 • 上一篇    下一篇

局部广义多粒度粗糙集

王虹,李敏赢   

  1. (山西师范大学数学与计算机科学学院,山西 临汾 041004)
  • 收稿日期:2019-09-23 修回日期:2020-02-07 接受日期:2020-08-25 出版日期:2020-08-25 发布日期:2020-08-29
  • 基金资助:
    山西省软科学(2017041016-4);山西省自然科学基金(201901D111280)

Local generalized multi-granulation rough set

WANG Hong,LI Min-ying   

  1. (School of Mathematics and Computer Science,Shanxi Normal University,Linfen 041004,China)
  • Received:2019-09-23 Revised:2020-02-07 Accepted:2020-08-25 Online:2020-08-25 Published:2020-08-29

摘要: 多粒度粗糙集的目标概念是一种由多个二元关系诱导的粒结构近似,是粗糙集领域的一个有价值的研究方向,在实际中得到了广泛的应用。然而,当数据集的规模很大时,会出现大量的未标记数据,计算目标概念的近似时需要计算所有对象的等价类,而且需要花费大量的时间来描述目标概念的近似以及复杂的计算过程,因此提出了局部广义多粒度粗糙集模型。首先通过引入特征函数来定义下近似和上近似;其次提出了一种用矩阵求解局部广义多粒度粗糙集下近似和上近似的方法,进一步研究了它们的性质;最后通过实例来验证所提模型的有效性,并给出了求局部广义多粒度粗糙集下近似的算法。此模型可以充分利用目标概念中的数据信息来处理数据,同时可以节省大量的计算时间。


关键词: 多粒度粗糙集, 局部粗糙集, 特征函数, 矩阵

Abstract: The target concept of multi-granulation rough sets is a kind of granular structure approximation induced by multiple binary relations, which is a valuable direction in the field of rough sets and has been widely used in practice. However, there are a lot of unlabeled data when the data set is large, and calculating the approximation of the target concept requires to calculate the equivalent class of all objects, which takes a lot of time to describe the approximation of the target concept as well as the complicated calculation process. Therefore, a local generalized multi-granulation rough set model is proposed. Firstly, the lower and upper approximations are defined by introducing characteristic functions. Secondly, a matrix method is proposed to solve the lower approximation and the upper approximation of the local generalized multi granularity rough set, and their properties are further studied. Finally, an example is given to verify the effectiveness of the proposed model, the algorithm to find the lower approximation of the local generalized multi granularity rough set is given. Besides, the model can make full use of the data information in the target concept to process data, which saves a lot of calculating time.


Key words: multi-granulation rough set, local rough set, characteristic function, matrix