Fig. 1: Three different formal concept lattices (FCLs) obtained from the three formal contexts describing the same 3BS, where balls are equipped with three distinct colours.
The General Concept Lattice (GCL) proposes a novel general construction of concept hierarchy from formal context, where the conventional Formal Concept Lattice based on Formal Concept Analysis (FCA) only serves as a substructure.[1][2][3]
The formal context is a data table of heterogeneous relations illustrating how objects carrying attributes. By analogy with truth-value table, every formal context can develop its fully extended version including all the columns corresponding to attributes constructed, by means of Boolean operations, out of the given attribute set. The GCL is based on the extended formal context which comprehends the full information content of the formal context in the sense that it incorporates whatever the formal context should consistently imply. Noteworthily, different formal contexts may give rise to the same extended formal context.[4]
^Wille, Rudolf (2005), "Formal Concept Analysis as Mathematical Theory of Concepts and Concept Hierarchies", Formal Concept Analysis, Lecture Notes in Computer Science, vol. 3626, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 1–33, doi:10.1007/11528784_1, ISBN 978-3-540-27891-7, S2CID 14153929, archived from the original on 2024-02-25, retrieved 2023-07-16
^Wille, Rudolf (1982), "Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts", Ordered Sets, Dordrecht: Springer Netherlands, pp. 445–470, doi:10.1007/978-94-009-7798-3_15, ISBN 978-94-009-7800-3, archived from the original on 2024-02-25, retrieved 2023-07-16
^Ganter, Bernhard; Wille, Rudolf (1999). Formal Concept Analysis. doi:10.1007/978-3-642-59830-2. ISBN 978-3-540-62771-5. S2CID 262487114. Archived from the original on 2024-02-25. Retrieved 2023-07-16.
^Cite error: The named reference :1 was invoked but never defined (see the help page).
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