On the Calculation of Formal Concept Stability

Abstract

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.