On Invariance of Concept Stability for Attribute Reduction in Concept Lattice

Formal Concept Analysis (FCA) methodology, as an efficient knowledge representation and knowledge discovery tool and has been widely used in various fields, such as data mining, expert systems, and others. Knowledge reduction is an essential issue for knowledge discovery. This paper focuses on attribute reduction in FCA and explores the internal relation between concept stability and attribute reduction. By observing the concept stability of concepts in original concept lattice and reduced concept lattice, a theorem about the invariance of concept stability for attribute reduction in concept lattice is presented and proved mathematically. It is believed that the proposed theorem provides a novel solution for quick attribute reduction and benefit for other social system applications.