ISSN 1000-1239 CN 11-1777/TP

• 人工智能 •

### 划分序乘积空间：基于划分的粒计算模型

1. 1(计算智能与信号处理教育部重点实验室(安徽大学) 合肥 230039); 2(安徽大学计算机科学与技术学院 合肥 230601); 3(里贾纳大学计算机科学系 加拿大里贾纳 S4S0A2) (xuyi1023@126.com)
• 出版日期: 2019-04-01
• 基金资助:
国家自然科学基金项目(61520106005，61761136014)；国家重点研发计划项目(2017YFB1010000)

### Partition Order Product Space: Partition Based Granular Computing Model

Xu Yi1,2, Yao Yiyu3

1. 1(Key Laboratory of Intelligent Computing and Signal Processing(Anhui University), Ministry of Education, Hefei 230039); 2(School of Computer Science and Technology, Anhui University, Hefei 230601); 3(Department of Computer Science, University of Regina, Regina, Canada S4S0A2)
• Online: 2019-04-01

Abstract: Granular computing solves complex problem based on granular structure. The existing studies on the granulation methods in granular structures mainly focus on multilevel granulation methods and multiview granulation methods respectively, without combining multilevel granulation methods and multiview granulation methods. Granular structure based on multilevel granulation methods is composed of a linearly ordered family of levels, which only provides one view with multiple levels. Granular structure based on multiview granulation methods provides multiple views, but each view only consists of one level. In order to understand and describe problem in a more comprehensive way, and then solve the problem more effectively and reasonably, given a universe, we take partition as the granulation method. Combining multilevel granulation methods with multiview granulation methods, we propose partition order product space. Firstly, using a partition on the universe to define a level. Secondly, using a nested sequence of partitions to define a hierarchy, which represents a view with linearly ordered relation. Finally, given a number of views determining a number of linearly ordered relations, based on the product of multiple linearly ordered relations, we propose partition order product space, which gives a granular computing model based on partition. Example demonstrates the superiority of partition order product space in real application.