Abstract
The influence of attribute ordering on the runtime efficiency of FCA algorithms has long been a subject of conjecture, yet no prior published work has directly addressed this issue. This paper proposes a novel approach, introducing criteria for ranking attribute importance within an L-fuzzy formal context. The primary objective is to reduce the runtime of concept lattice construction algorithms by strategically reordering attributes based on these criteria.
This work has been partially funded by the State Agency of Research (AEI), the Ministerio de Ciencia, Innovación y Universidades (MCIU), the European Social Research Fund (FEDER), the Junta de Andalucía (JA), y la Universidad de Málaga (UMA) through the PhD contract FPU19/01467 (MCIU), the VALID research project (PID2022-140630NB-I00 funded by MCIN/AEI/10.13039/501100011033) and the research project PID2021-127870OB-I00 (MCIU/AEI/FEDER, UE).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Andrews, S.: In-Close, a fast algorithm for computing formal concepts. In: Proceedings of the International Conference on Conceptual Structures, Moscow (2009)
Andrews, S.: Making use of empty intersections to improve the performance of CbO-type algorithms. In: Bertet, K., Borchmann, D., Cellier, P., Ferre, S. (eds.) Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10308. LNAI, pp. 56–71. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59271-8_4
Andrews, S.: A new method for inheriting canonicity test failures in close-by-one type algorithms. In: Ignatov, D.I., Nourine, L. (eds.) Proceedings of the Fourteenth International Conference on Concept Lattices and Their Applications, CLA 2018, Olomouc, Czech Republic, 12–14 June 2018. CEUR Workshop Proceedings, vol. 2123, pp. 255–266. CEUR-WS.org (2018). https://ceur-ws.org/Vol-2123/paper21.pdf
Aragón, R.G., Medina, J., Ramírez-Poussa, E.: Factorizing formal contexts from closures of necessity operators. Comput. Appl. Math. 43, 1–32 (2024). https://doi.org/10.1016/j.ins.2022.05.047
Bělohávek, R., De Baets, B., Outrata, J., Vychodil, V.: Computing the lattice of all fixpoints of a fuzzy closure operator. IEEE Trans. Fuzzy Syst. 18(3), 546–557 (2010). https://doi.org/10.1109/TFUZZ.2010.2041006
Bělohlávek, R.: Fuzzy Relational Systems. Springer, Cham (2002). https://doi.org/10.1007/978-1-4615-0633-1
Bělohlávek, R.: Algorithms for fuzzy concept lattices. In: International Conference on Recent Advances in Soft Computing, pp. 200–205 (2002)
Bělohlávek, R., Konečny, J.: Fixpoints of fuzzy closure operators via ordinary algorithms. In: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1–6 (2017). https://doi.org/10.1109/FUZZ-IEEE.2017.8015676
Burusco-Juandeaburre, A., Fuentes-González, R.: The study of the L-fuzzy concept lattice. Mathware Soft Comput. 1(3), 209–218 (1994)
Cordero, P., Enciso, M., López Rodríguez, D., Mora, Á.: fcaR, formal concept analysis with R. R J. 14, 341–361 (2022)
Ganter, B.: Two basic algorithms in concept analysis. In: Kwuida, L., Sertkaya, B. (eds.) Formal Concept Analysis: 8th International Conference, ICFCA 2010, Agadir, Morocco, 15–18 March 2010, Proceedings 8, pp. 312–340. Springer, Cham (2010). https://doi.org/10.1007/978-3-642-11928-6_22
Guigues, J.L., Duquenne, V.: Familles minimales d’implications informatives résultant d’un tableau de données binaires. Mathématiques et Sciences humaines 95, 5–18 (1986)
Hanika, T., Hirth, J.: Conexp-Clj - a research tool for FCA. ICFCA (Suppl.) 2378, 70–75 (2019)
Johnson, D.S., Yannakakis, M., Papadimitriou, C.H.: On generating all maximal independent sets. Inf. Process. Lett. 27(3), 119–123 (1988). https://doi.org/10.1016/0020-0190(88)90065-8
Krajča, P., Outrata, J., Vychodil, V.: Advances in algorithms based on CbO. In: CLA, vol. 672, pp. 325–337. Citeseer (2010)
Kuznetsov, S.: A fast algorithm for computing all intersections of objects in a finite semi-lattice. Autom. Documentation Math. Linguist. 27, 11–21 (1993)
Kuznetsov, S.O.: Interpretation on graphs and complexity characteristics of a search for specific patterns. Autom. Documentation Math. Linguist. 24(1), 37–45 (1989)
Kuznetsov, S.O.: A fast algorithm for computing all intersections of objects from an arbitrary semilattice. Nauchno-Tekhnicheskaya Informatsiya Seriya 2-Informatsionnye Protsessy i Sistemy (1), 17–20 (1993)
Pattison, T., Nataraja, A.: Doubly-lexical order supports standardisation and recursive partitioning of formal context. In: Dürrschnabel, D., López Rodríguez, D. (eds.) International Conference on Formal Concept Analysis, pp. 17–32. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-35949-1_2
R Core Team: R: A Language and Environment for Statistical Computing (2019). https://www.r-project.org/
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Springer, Cham (1982). https://doi.org/10.1007/978-94-009-7798-3_15
Yao, W., Lu, L.X.: Fuzzy Galois connections on fuzzy posets. Math. Log. Q. 55, 105–112 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
López-Rodríguez, D., Ojeda-Hernández, M. (2024). Rearrangement of Fuzzy Formal Contexts for Reducing Cost of Algorithms. In: Cabrera, I.P., Ferré, S., Obiedkov, S. (eds) Conceptual Knowledge Structures. CONCEPTS 2024. Lecture Notes in Computer Science(), vol 14914. Springer, Cham. https://doi.org/10.1007/978-3-031-67868-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-031-67868-4_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-67867-7
Online ISBN: 978-3-031-67868-4
eBook Packages: Computer ScienceComputer Science (R0)