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Journal of Applied Mathematics
Volume 2014, Article ID 917639, 6 pages
Research Article

On the Calculation of Formal Concept Stability

School of Computer Science and Technology, Henan Polytechnic University, No. 2001, ShiJi Avenue, Jiaozuo 454000, China

Received 27 January 2014; Revised 15 June 2014; Accepted 29 June 2014; Published 10 July 2014

Academic Editor: Heping Zhang

Copyright © 2014 Hui-lai Zhi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The idea of stability has been used in many applications. However, computing stability is still a challenge and the best algorithms known so far have algorithmic complexity quadratic to the size of the lattice. To improve the effectiveness, a critical term is introduced in this paper, that is, minimal generator, which serves as the minimal set that makes a concept stable when deleting some objects from the extent. Moreover, by irreducible elements, minimal generator is derived. Finally, based on inclusion-exclusion principle and minimal generator, formulas for the calculation of concept stability are proposed.