On basic conditions to generate multi-adjoint concept lattices via Galois connections

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Authors

Juan Carlos Díaz-Moreno

Jesús Medina

Manuel Ojeda-Aciego

Published

1 January 2014

Publication details

Int. J. Gen. Syst. vol. 43 (2), pages 149–161.

Links

Abstract

This paper introduces sufficient and necessary conditions with respect to the fuzzy operators considered in a multi-adjoint frame under which the standard combinations of multi-adjoint sufficiency, possibility, and necessity operators form (antitone or isotone) Galois connections. The underlying idea is to study the minimal algebraic requirements so that the concept-forming operators (defined using the same syntactical form than the extension and intension operators of multi-adjoint concept lattices) form a Galois connection. As a consequence, given a relational database, we have much more possibilities to construct concept lattices associated with it, so that we can choose the specific version which better suits the situation.

Citation

Please, cite this work as:

[DMO14] J. C. D'-Moreno, J. Medina, and M. Ojeda-Aciego. “On basic conditions to generate multi-adjoint concept lattices via Galois connections”. In: Int. J. Gen. Syst. 43.2 (2014), pp. 149-161. DOI: 10.1080/03081079.2013.879302. URL: https://doi.org/10.1080/03081079.2013.879302.

BibTeX

@Article{DiazMoreno2014,
     author = {Juan Carlos D'-Moreno and Jes{’u}s Medina and Manuel Ojeda-Aciego},
     journal = {Int. J. Gen. Syst.},
     title = {On basic conditions to generate multi-adjoint concept lattices via Galois connections},
     year = {2014},
     number = {2},
     pages = {149–161},
     volume = {43},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/journals/ijgs/Diaz-MorenoMO14.bib},
     doi = {10.1080/03081079.2013.879302},
     timestamp = {Thu, 07 Jan 2021 00:00:00 +0100},
     url = {https://doi.org/10.1080/03081079.2013.879302},
}

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Citations
CrossRef - Citation Indexes: 8
Scopus - Citation Indexes: 22

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Mendeley - Readers: 8

Cites

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Papers citing this work

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

[1] L. Antoni, S. Krajči, and O. Krídlo. “Constraint heterogeneous concept lattices and concept lattices with heterogeneous hedges”. In: Fuzzy Sets and Systems 303 (Nov. 2016), p. 21–37. ISSN: 0165-0114. DOI: 10.1016/j.fss.2015.12.007. URL: http://dx.doi.org/10.1016/j.fss.2015.12.007.

[2] L. Antoni, S. Krajči, and O. Krídlo. “On Fuzzy Generalizations of Concept Lattices”. In: Interactions Between Computational Intelligence and Mathematics. Springer International Publishing, 2018, p. 79–103. ISBN: 9783319746814. DOI: 10.1007/978-3-319-74681-4_6. URL: http://dx.doi.org/10.1007/978-3-319-74681-4_6.

[3] L. Antoni, S. Krajči, and O. Krídlo. “Representation of fuzzy subsets by Galois connections”. In: Fuzzy Sets and Systems 326 (Nov. 2017), p. 52–68. ISSN: 0165-0114. DOI: 10.1016/j.fss.2017.05.020. URL: http://dx.doi.org/10.1016/j.fss.2017.05.020.

[4] R. G. Aragón, J. Medina, and E. Ramírez-Poussa. “Characterization of the Infimum of Classes Induced by an Attribute Reduction in FCA”. In: Computational Intelligence and Mathematics for Tackling Complex Problems 3. Springer International Publishing, Aug. 2021, p. 73–79. ISBN: 9783030749705. DOI: 10.1007/978-3-030-74970-5_9. URL: http://dx.doi.org/10.1007/978-3-030-74970-5_9.

[5] R. G. Aragón, J. Medina, and E. Ramírez-Poussa. “Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA”. In: Mathematics 9.5 (Mar. 2021), p. 565. ISSN: 2227-7390. DOI: 10.3390/math9050565. URL: http://dx.doi.org/10.3390/math9050565.

[6] J. Atif, I. Bloch, and C. Hudelot. “Some Relationships Between Fuzzy Sets, Mathematical Morphology, Rough Sets, F-Transforms, and Formal Concept Analysis”. In: International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 24.Suppl. 2 (Dec. 2016), p. 1–32. ISSN: 1793-6411. DOI: 10.1142/s0218488516400080. URL: http://dx.doi.org/10.1142/s0218488516400080.

[7] I. P. Cabrera, P. Cordero, E. Muñoz-Velasco, et al. “Galois Connections Between Unbalanced Structures in a Fuzzy Framework”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer International Publishing, 2020, p. 736–747. ISBN: 9783030501532. DOI: 10.1007/978-3-030-50153-2_54. URL: http://dx.doi.org/10.1007/978-3-030-50153-2_54.

[8] M. E. Cornejo Piñero, J. Medina-Moreno, and E. Ramírez-Poussa. “General Negations for Residuated Fuzzy Logics”. In: Rough Sets and Current Trends in Soft Computing. Springer International Publishing, 2014, p. 13–22. ISBN: 9783319086446. DOI: 10.1007/978-3-319-08644-6_2. URL: http://dx.doi.org/10.1007/978-3-319-08644-6_2.

[9] M. E. Cornejo, L. Fariñas del Cerro, and J. Medina. “Multi-adjoint lattice logic and truth-stressing hedges”. In: Fuzzy Sets and Systems 445 (Sep. 2022), p. 43–65. ISSN: 0165-0114. DOI: 10.1016/j.fss.2022.03.006. URL: http://dx.doi.org/10.1016/j.fss.2022.03.006.

[10] M. E. Cornejo, J. Medina, and F. J. Ocaña. “Attribute implications in multi-adjoint concept lattices with hedges”. In: Fuzzy Sets and Systems 479 (Mar. 2024), p. 108854. ISSN: 0165-0114. DOI: 10.1016/j.fss.2023.108854. URL: http://dx.doi.org/10.1016/j.fss.2023.108854.

[11] M. E. Cornejo, J. Medina, and E. Ramírez-Poussa. “Adjoint negations, more than residuated negations”. In: Information Sciences 345 (Jun. 2016), p. 355–371. ISSN: 0020-0255. DOI: 10.1016/j.ins.2016.01.038. URL: http://dx.doi.org/10.1016/j.ins.2016.01.038.

[12] M. E. Cornejo, J. Medina, and E. Ramírez-Poussa. “Adjoint Triples and Residuated Aggregators”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer International Publishing, 2014, p. 345–354. ISBN: 9783319088525. DOI: 10.1007/978-3-319-08852-5_36. URL: http://dx.doi.org/10.1007/978-3-319-08852-5_36.

[13] M. E. Cornejo, J. Medina, and E. Ramírez-Poussa. “Algebraic structure and characterization of adjoint triples”. In: Fuzzy Sets and Systems 425 (Nov. 2021), p. 117–139. ISSN: 0165-0114. DOI: 10.1016/j.fss.2021.02.002. URL: http://dx.doi.org/10.1016/j.fss.2021.02.002.

[14] M. E. Cornejo, J. Medina, and E. Ramírez-Poussa. “Multi-adjoint algebras versus non-commutative residuated structures”. In: International Journal of Approximate Reasoning 66 (Nov. 2015), p. 119–138. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2015.08.003. URL: http://dx.doi.org/10.1016/j.ijar.2015.08.003.

[15] M. E. Cornejo, J. Medina, E. Ramírez-Poussa, et al. “Preferences in discrete multi-adjoint formal concept analysis”. In: Information Sciences 650 (Dec. 2023), p. 119507. ISSN: 0020-0255. DOI: 10.1016/j.ins.2023.119507. URL: http://dx.doi.org/10.1016/j.ins.2023.119507.

[16] J. C. Díaz-Moreno, J. Medina, and E. Turunen. “Computing the minimal solutions of finite fuzzy relation equations on lineal carriers”. In: Position Papers of the 2016 Federated Conference on Computer Science and Information Systems. Vol. 9. FedCSIS 2016. PTI, Oct. 2016, p. 19–23. DOI: 10.15439/2016f564. URL: http://dx.doi.org/10.15439/2016f564.

[17] J. C. Diaz, N. Madrid, J. Medina, et al. “New links between mathematical morphology and fuzzy property-oriented concept lattices”. In: 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, Jul. 2014, p. 599–603. DOI: 10.1109/fuzz-ieee.2014.6891882. URL: http://dx.doi.org/10.1109/fuzz-ieee.2014.6891882.

[18] P. Eklund, M. Á. Galán García, J. Kortelainen, et al. “Monadic Formal Concept Analysis”. In: Rough Sets and Current Trends in Soft Computing. Springer International Publishing, 2014, p. 201–210. ISBN: 9783319086446. DOI: 10.1007/978-3-319-08644-6_21. URL: http://dx.doi.org/10.1007/978-3-319-08644-6_21.

[19] J. Konecny and M. Ojeda-Aciego. “On homogeneousL-bonds and heterogeneousL-bonds”. In: International Journal of General Systems 45.2 (Oct. 2015), p. 160–186. ISSN: 1563-5104. DOI: 10.1080/03081079.2015.1072926. URL: http://dx.doi.org/10.1080/03081079.2015.1072926.

[20] O. Kridlo and M. Ojeda-Aciego. “Extending formal concept analysis using intuitionistic l-fuzzy sets”. In: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, Jul. 2017, p. 1–6. DOI: 10.1109/fuzz-ieee.2017.8015570. URL: http://dx.doi.org/10.1109/fuzz-ieee.2017.8015570.

[21] D. Lobo, V. López-Marchante, and J. Medina. “Approximating Fuzzy Relation Equations Through Concept Lattices”. In: Formal Concept Analysis. Springer Nature Switzerland, 2023, p. 3–16. ISBN: 9783031359491. DOI: 10.1007/978-3-031-35949-1_1. URL: http://dx.doi.org/10.1007/978-3-031-35949-1_1.

[22] N. Madrid, J. Medina, M. Ojeda-Aciego, et al. “Toward the Use of Fuzzy Relations in the Definition of Mathematical Morphology Operators”. In: Journal of Fuzzy Set Valued Analysis 2016.1 (2016), p. 87–98. ISSN: 2193-4169. DOI: 10.5899/2016/jfsva-00270. URL: http://dx.doi.org/10.5899/2016/jfsva-00270.

[23] V. Vychodil. “Parameterizing the Semantics of Fuzzy Attribute Implications by Systems of Isotone Galois Connections”. In: IEEE Transactions on Fuzzy Systems 24.3 (Jun. 2016), p. 645–660. ISSN: 1941-0034. DOI: 10.1109/tfuzz.2015.2470530. URL: http://dx.doi.org/10.1109/tfuzz.2015.2470530.