Direct-optimal basis computation by means of the fusion of simplification rules

 

Abstract

The importance of the computation of direct bases of implications has been motivated by several authors in different areas. They emphasize the use of direct bases in several problems, where a large number of closures are needed. The more efficient the basis computation is, the better performance the methods solving these problems has. Here, we propose a new method, named SLgetdo, to calculate the direct-optimal basis. The main characteristic of SLgetdo is the full integration of simplification paradigm, providing a limited rise of the implicational set throughout its execution. We have showed the better behavior of SLgetdo in an empirical experiment. The general conclusion is that it improves the performance of previous methods, providing a better management of time and space resources.

Citation

Please, cite this work as:

[Rod+18] E. Rodríguez-Lorenzo, K. Bertet, P. Cordero, et al. “Direct-optimal basis computation by means of the fusion of simplification rules”. In: Discrete Applied Mathematics 249 (2018). Concept Lattices and Applications: Recent Advances and New Opportunities, pp. 106-119. ISSN: 0166-218X. DOI: https://doi.org/10.1016/j.dam.2017.12.031. URL: https://www.sciencedirect.com/science/article/pii/S0166218X1730611X.

BibTeX

@article{RODRIGUEZLORENZO2018106,
    title = {Direct-optimal basis computation by means of the fusion of simplification rules},
    journal = {Discrete Applied Mathematics},
    volume = {249},
    pages = {106-119},
    year = {2018},
    note = {Concept Lattices and Applications: Recent Advances and New Opportunities},
    issn = {0166-218X},
    doi = {https://doi.org/10.1016/j.dam.2017.12.031},
    url = {https://www.sciencedirect.com/science/article/pii/S0166218X1730611X},
    author = {Estrella Rodríguez-Lorenzo and Karell Bertet and Pablo Cordero and Manuel Enciso and Ángel Mora},
    keywords = {Direct-optimal basis, Closure, Simplification Logic},
    abstract = {The importance of the computation of direct bases of implications has been motivated by several authors in different areas. They emphasize the use of direct bases in several problems, where a large number of closures are needed. The more efficient the basis computation is, the better performance the methods solving these problems has. Here, we propose a new method, named SLgetdo, to calculate the direct-optimal basis. The main characteristic of SLgetdo is the full integration of simplification paradigm, providing a limited rise of the implicational set throughout its execution. We have showed the better behavior of SLgetdo in an empirical experiment. The general conclusion is that it improves the performance of previous methods, providing a better management of time and space resources.}
}

Bibliometric data

The following data has been extracted from resources such as OpenAlex, Dimensions, PlumX or Altmetric.

9

CITATIONS

9 Total citations

1 Recent citation

3.15 Field Citation Ratio

n/a Relative Citation Ratio

• Citations
• CrossRef - Citation Indexes: 7
• Scopus - Citation Indexes: 8

• Captures
• Mendeley - Readers: 7

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Cites

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Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

[1] P. Cordero, M. Enciso, A. Mora, et al. “Interactive Search by Using Minimal Generators”. In: Computational Intelligence and Mathematics for Tackling Complex Problems 2. Springer International Publishing, 2022, p. 147–153. ISBN: 9783030888176. DOI: 10.1007/978-3-030-88817-6_17. URL: http://dx.doi.org/10.1007/978-3-030-88817-6_17.

[2] P. Cordero, M. Enciso, Á. Mora, et al. “A Formal Concept Analysis Approach to Cooperative Conversational Recommendation”. In: International Journal of Computational Intelligence Systems 13.1 (2020), p. 1243. ISSN: 1875-6883. DOI: 10.2991/ijcis.d.200806.001. URL: http://dx.doi.org/10.2991/ijcis.d.200806.001.

[3] M. E. Cornejo, J. Medina, and C. Rubio-Manzano. “Formal Analysis of Solar Power and Weather Data”. In: Computational Intelligence and Mathematics for Tackling Complex Problems 2. Springer International Publishing, 2022, p. 81–89. ISBN: 9783030888176. DOI: 10.1007/978-3-030-88817-6_10. URL: http://dx.doi.org/10.1007/978-3-030-88817-6_10.

[4] D. Dubois, J. Medina, and H. Prade. “Extracting attribute implications from a formal context: Unifying the basic approaches”. In: Information Sciences 689 (Jan. 2025), p. 121419. ISSN: 0020-0255. DOI: 10.1016/j.ins.2024.121419. URL: http://dx.doi.org/10.1016/j.ins.2024.121419.

[5] D. Dubois, J. Medina, H. Prade, et al. “Disjunctive attribute dependencies in formal concept analysis under the epistemic view of formal contexts”. In: Information Sciences 561 (Jun. 2021), p. 31–51. ISSN: 0020-0255. DOI: 10.1016/j.ins.2020.12.085. URL: http://dx.doi.org/10.1016/j.ins.2020.12.085.

[6] D. López-Rodríguez, E. Muñoz-Velasco, and M. Ojeda-Aciego. “Formal Methods in FCA and Big Data”. In: Complex Data Analytics with Formal Concept Analysis. Springer International Publishing, Dec. 2021, p. 201–224. ISBN: 9783030932787. DOI: 10.1007/978-3-030-93278-7_9. URL: http://dx.doi.org/10.1007/978-3-030-93278-7_9.

[7] M. Ojeda-Hernández, I. P. Cabrera, and P. Cordero. “Quasi-closed elements in fuzzy posets”. In: Journal of Computational and Applied Mathematics 404 (Apr. 2022), p. 113390. ISSN: 0377-0427. DOI: 10.1016/j.cam.2021.113390. URL: http://dx.doi.org/10.1016/j.cam.2021.113390.

[8] T. Pattison, M. Enciso, Á. Mora, et al. “Scalable Visual Analytics in FCA”. In: Complex Data Analytics with Formal Concept Analysis. Springer International Publishing, Dec. 2021, p. 167–200. ISBN: 9783030932787. DOI: 10.1007/978-3-030-93278-7_8. URL: http://dx.doi.org/10.1007/978-3-030-93278-7_8.

[9] F. Pérez-Gámez, D. López-Rodríguez, P. Cordero, et al. “Simplifying Implications with Positive and Negative Attributes: A Logic-Based Approach”. In: Mathematics 10.4 (Feb. 2022), p. 607. ISSN: 2227-7390. DOI: 10.3390/math10040607. URL: http://dx.doi.org/10.3390/math10040607.