A new algebraic structure for formal concept analysis

Authors:
Lidong Wang;Xiaodong Liu;Jiannong Cao
Affiliations:
Department of Mathematics, Dalian Maritime University, Dalian 116026, PR China;Department of Mathematics, Dalian Maritime University, Dalian 116026, PR China and Research Center of Information and Control, Dalian University of Technology, Dalian 116024, PR China;Department of Computing, Hong Kong Polytechnic University, Kowloon, Hong Kong
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

Formal concept analysis (FCA) originally proposed by Wille [39], is an important theory for data analysis and knowledge discovery. Concept lattice is the core of the mathematical theory of formal concept analysis. To address the requirements of real word applications, concept lattice has been extended to many other forms from the theoretical point of view and possible applications. In this paper, with the aim of deriving the mathematical properties of formal concepts from the point of algebra, we propose a new algebra system for the formal context. Under the frame of the proposed system, some interesting properties of formal concepts are explored, which could be applied to explore concept hierarchy and ontology merging.