A categorical representation of algebraic domains based on variations of rough approximable concepts

作者：Guo, Lankun; Li, Qingguo^*; Huang, Mengqiao

来源：International Journal of Approximate Reasoning, 2014, 55(3): 885-895.

DOI：10.1016/j.ijar.2013.09.008

• Rough approximable concept
• Rough pseudo-concept
• Hyper-context
• Hyper-concept
• Algebraic domain

In this paper, we propose two variations of rough approximable concepts and investigate the order-theoretic properties of the associated concept hierarchies. We first show that every rough pseudo-concept hierarchy is a completely distributive lattice and its completely compact elements are exactly the rough pseudo-concepts generated from individual attributes. Next, we propose the notions of hyper-contexts and hyper-concepts, and prove that they provide an approach to restructuring algebraic domains. Finally, we set hyper-contexts into a category in which hyper-mappings serve as the morphisms. It turns out that this category is precisely equivalent to that of algebraic domains.

• 出版日期2014-3
• 单位湖南涉外经济学院; 湖南大学