Abstract

Granular computing is a widely used computational paradigm nowadays. Particularly, within the rough set theory, granular computing plays a key role. In this paper, we propose a generic approach of rough sets, the granular extended multigranular sets (GEMS) for dealing with both mixed and incomplete information systems. Not only our proposal does use the traditional optimistic and pessimistic granulations with respect to single attributes, but also we introduce granulations with respect to attribute sets, as well as two new ways of granulating: the optimistic + pessimistic granulation and the pessimistic + optimistic granulation. In addition, we have developed a particular case of the proposed GEMS: the multigranular maximum similarity rough sets (MMSRS). We have proved some of the properties of the MMSRS, and we tested its effectiveness with respect to other existing granular rough sets models. The experimental results show the flexibility and the capabilities of the proposed model, while handling mixed and incomplete information systems.

中文翻译：

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混合和不完整信息系统的通用扩展多粒度集

摘要

粒度计算是当今广泛使用的计算范例。特别是在粗糙集理论中，粒度计算起着关键作用。在本文中，我们提出了一种粗糙集的通用方法，即用于同时处理混合信息系统和不完整信息系统的粒度扩展多粒度集（GEMS）。我们的建议不仅针对单个属性使用了传统的乐观和悲观粒度，而且针对属性集引入了粒度，以及两种新的粒度方法：乐观+悲观粒度和悲观+乐观粒度。此外，我们已经开发了提出的GEMS的特殊情况：多颗粒最大相似度粗糙集（MMSRS）。我们已经证明了MMSRS的某些特性，我们针对其他现有的粒状粗糙集模型测试了其有效性。实验结果表明了该模型的灵活性和功能，同时能够处理混合和不完整的信息系统。