×

Boolean substructures in formal concept analysis. (English) Zbl 07493551

Braud, Agnès (ed.) et al., Formal concept analysis. 16th international conference, ICFCA 2021, Strasbourg, France, June 29 – July 2, 2021. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12733, 38-53 (2021).
Summary: It is known that a (concept) lattice contains an n-dimensional Boolean suborder if and only if the context contains an n-dimensional contra-nominal scale as subcontext. In this work, we investigate more closely the interplay between the Boolean subcontexts of a given finite context and the Boolean suborders of its concept lattice. To this end, we define mappings from the set of subcontexts of a context to the set of suborders of its concept lattice and vice versa and study their structural properties. In addition, we introduce closed-subcontexts as an extension of closed relations to investigate the set of all sublattices of a given lattice.
For the entire collection see [Zbl 1482.68011].

MSC:

68T30 Knowledge representation
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Albano, A.: Polynomial growth of concept lattices, canonical bases and generators: extremal set theory in formal concept analysis. Ph.D. thesis, SLUB Dresden (2017)
[2] Albano, A.: Rich subcontexts. arXiv preprint arXiv:1701.03478 (2017)
[3] Albano, A., Chornomaz, B.: Why concept lattices are large - extremal theory for the number of minimal generators and formal concepts. In: International Conference on Concept Lattices and Their Applications. CEUR Workshop Proceedings, vol. 1466, pp. 73-86. CEUR-WS.org (2015)
[4] Dias, S.M., Vieira, N.: Reducing the size of concept lattices: the JBOS approach. In: International Conference on Concept Lattices and Their Applications. CEUR Workshop Proceedings, vol. 672, pp. 80-91. CEUR-WS.org (2010)
[5] Felde, M.; Hanika, T.; Endres, D.; Alam, M.; Şotropa, D., Formal context generation using Dirichlet distributions, Graph-Based Representation and Reasoning, 57-71 (2019), Cham: Springer, Cham
[6] Ganter, B.; Kuznetsov, SO; Medina, R.; Obiedkov, S., Scale coarsening as feature selection, Formal Concept Analysis, 217-228 (2008), Heidelberg: Springer, Heidelberg · Zbl 1131.68536
[7] Ganter, B.; Wille, R., Formal Concept Analysis - Mathematical Foundations (1999), Heidelberg: Springer, Heidelberg · Zbl 0909.06001
[8] Hanika, T.; Koyda, M.; Stumme, G.; Endres, D.; Alam, M.; Şotropa, D., Relevant attributes in formal contexts, Graph-Based Representation and Reasoning, 102-116 (2019), Cham: Springer, Cham
[9] Kauer, M.; Krupka, M., Generating complete sublattices by methods of formal concept analysis, Int. J. Gen Syst, 46, 5, 475-489 (2017)
[10] Kuznetsov, S.: Stability as an estimate of the degree of substantiation of hypotheses derived on the basis of operational similarity. Autom. Doc. Math. Linguist. 24 (1990) · Zbl 0737.68069
[11] Liu, J., Paulsen, S., Sun, X., Wang, W., Nobel, A.B., Prins, J.F.: Mining approximate frequent itemsets in the presence of noise: algorithm and analysis. In: International Conference on Data Mining, pp. 407-418 (2006)
[12] Qi, J.; Wei, L.; Wan, Q., Multi-level granularity in formal concept analysis, Granular Comput., 4, 3, 351-362 (2018)
[13] Stumme, G.; Taouil, R.; Bastide, Y.; Pasquier, N.; Lakhal, L., Computing iceberg concept lattices with titanic, Data Knowl. Eng., 42, 2, 189-222 (2002) · Zbl 0996.68046
[14] Wille, R.: Bedeutungen von Begriffsverbänden. In: Beiträge zur Begriffsanalyse, pp. 161-211. B.I.-Wissenschaftsverlag, Mannheim (1987)
[15] Zadeh, LA, Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets Syst., 90, 2, 111-127 (1997) · Zbl 0988.03040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.