Partition Order Product Space: Partition Based Granular Computing Model

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.