Concept lattice restoration based on concept reducts

The concept lattice restoration methods are investigated through concept reducts. First, the relationship between subsets of concept reducts and meet-irreducible concepts is established, thereby revealing the connection between concept reducts and meet-irreducible concept sets. Based on this foundation, a concept lattice restoration method is proposed in which supremums are first computed, followed by infimums, for formal concepts in concept reducts. Dually, an alternative restoration approach is presented in which infimums are first computed, then supremums. It is demonstrated that concept lattices can be restored by concept reducts using partial formal concepts, thereby achieving effective compression and storage of lattice information. This provides practical significance and potential application value for concept reduction.