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

Authors:
Lankun Guo;Qingguo Li;Mengqiao Huang
Affiliations:
College of Information Science and Engineering, Hunan University, Changsha, Hunan 410012, PR China;College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China;Faculty of Science, Hunan International Economics University, Changsha, Hunan 410205, PR China
Venue:
International Journal of Approximate Reasoning
Year:
2014

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Abstract

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.