Determination and description problems are two basic problems of Formal Concept Analysis (FCA). Since most methods of determining the concept lattice are based on generation of non-neighbor concepts, the process of analyzing the neighboring relation between generated concepts is required to solve the description problem.
Pak Chol Hong, a researcher at the Faculty of Applied Mathematics, has proposed some new efficient algorithms for simultaneously describing the concept lattice and its hierarchy-matrix without this process. The hierarchy-matrix is a successful description of the concept lattice, by which any software can autonomously understand the information of hierarchy of the concepts. The focus of his algorithms is on generation of neighbor concepts tested for canonicity and registering the neighbor information in the hierarchy-matrix sequentially.
He drew the following conclusions.
First, the concepts of subcontexts induced by a given concept are lower (or upper) ones of the concept and all lower (or upper) neighbor concepts of the concept are denoted by the antitone Galois connections on the subcontexts.
Second, all lower (or upper) neighbor concepts of a given concept are generated by the antitone Galois connections on the subcontexts and restricted by the rank of the subcontex-matrices.
Third, the key aspects of the efficiency of the concept lattice and its hierarchy-matrix based on the generation of lower neighbor concepts (BCLHMLN) and the concept lattice and its hierarchy-matrix based on the generation of upper neighbor concepts (BCLHMUN) are generation of neighbor concepts on the subcontext, the equivalence class of the object or the attribute with respect to adjoin mappings of Galois connections, the design of canonicity test and the utilization of the histories of generated lower (or upper) concepts.
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