徐怡, 姚一豫. 划分序乘积空间：基于划分的粒计算模型[J]. 计算机研究与发展, 2019, 56(4): 836-843.
 引用本文: 徐怡, 姚一豫. 划分序乘积空间：基于划分的粒计算模型[J]. 计算机研究与发展, 2019, 56(4): 836-843.
Xu Yi, Yao Yiyu. Partition Order Product Space: Partition Based Granular Computing Model[J]. Journal of Computer Research and Development, 2019, 56(4): 836-843.
 Citation: Xu Yi, Yao Yiyu. Partition Order Product Space: Partition Based Granular Computing Model[J]. Journal of Computer Research and Development, 2019, 56(4): 836-843.

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

• 摘要: 粒计算(granular computing)通过粒结构实现复杂问题求解. 现有对粒结构中粒化方法的研究，主要是分别基于多层次的粒化方法和基于多视角的粒化方法，没有将多层次粒化方法和多视角粒化方法结合起来.基于多层次的粒化方法得到的粒结构由一个满足线性序关系的多个层构成，即单视角多层次.基于多视角的粒化方法得到的粒结构具有多个视角，但是每个视角仅有一个层.为了更全面地理解和描述问题，从而可以更有效和合理地解决问题，给定一个论域，使用划分作为粒化方法，将多层次的粒化方法和多视角的粒化方法相结合，定义划分序乘积空间.首先，使用论域上的一个划分定义一个层.其次，使用一个嵌套的划分序定义一个多层次，表示为一个视角，层和层之间具有线性序关系.最后，给定多个视角，则定义了多个线性序关系，基于多个线性序关系的乘积，定义划分序乘积空间.划分序乘积空间给出了一种基于划分的粒计算模型.通过实例说明了划分序乘积空间在实际应用中的优越性.

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.

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