On Multi-adjoint Concept Lattices: Definition and Representation Theorem

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Authors

Jesús Medina

Jorge Ruiz-Calvi~no

Published

1 January 2007

Publication details

Formal Concept Analysis, 5th International Conference, {ICFCA} 2007, Clermont-Ferrand, France, February 12-16, 2007, Proceedings , Lecture Notes in Computer Science vol. 4390, pages 197–209.

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Abstract

Citation

Please, cite this work as:

[MOR07] J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calvi~no. “On Multi-adjoint Concept Lattices: Definition and Representation Theorem”. In: Formal Concept Analysis, 5th International Conference, ICFCA 2007, Clermont-Ferrand, France, February 12-16, 2007, Proceedings. Ed. by S. O. Kuznetsov and S. Schmidt. Vol. 4390. Lecture Notes in Computer Science. Springer, 2007, pp. 197-209. DOI: 10.1007/978-3-540-70901-5_13. URL: https://doi.org/10.1007/978-3-540-70901-5_13.

BibTeX

@InProceedings{Medina2007b,
     author = {Jes{’u}s Medina and Manuel Ojeda-Aciego and Jorge Ruiz-Calvi~no},
     booktitle = {Formal Concept Analysis, 5th International Conference, {ICFCA} 2007, Clermont-Ferrand, France, February 12-16, 2007, Proceedings},
     title = {On Multi-adjoint Concept Lattices: Definition and Representation Theorem},
     year = {2007},
     editor = {Sergei O. Kuznetsov and Stefan Schmidt},
     pages = {197–209},
     publisher = {Springer},
     series = {Lecture Notes in Computer Science},
     volume = {4390},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/conf/icfca/MedinaOR07.bib},
     doi = {10.1007/978-3-540-70901-5_13},
     timestamp = {Sun, 06 Oct 2024 01:00:00 +0200},
     url = {https://doi.org/10.1007/978-3-540-70901-5_13},
}

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On Multi-adjoint Concept Lattices: Definition and Representation Theorem

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Papers citing this work

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

[1] C. Alcalde, A. Burusco, and R. Fuentes-Gonzalez. “On the solutions of L-fuzzy relational equations with sub-triangle composition and its relation with the L-Fuzzy Concept Theory”. In: Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011). EUSFLAT-2011 and LFA-2011. Atlantis Press, 2011. DOI: 10.2991/eusflat.2011.96. URL: http://dx.doi.org/10.2991/eusflat.2011.96.

[2] C. Alcalde, A. Burusco, and R. Fuentes-González. “Obtaining Significant Relations in L-Fuzzy Contexts”. In: Trends in Applied Intelligent Systems. Springer Berlin Heidelberg, 2010, p. 183–192. ISBN: 9783642130250. DOI: 10.1007/978-3-642-13025-0_20. URL: http://dx.doi.org/10.1007/978-3-642-13025-0_20.

[3] C. Alcalde, A. Burusco, and R. Fuentes-González. “Some Results on the Composition of L-Fuzzy Contexts”. In: Advances in Computational Intelligence. Springer Berlin Heidelberg, 2012, p. 305–314. ISBN: 9783642317156. DOI: 10.1007/978-3-642-31715-6_33. URL: http://dx.doi.org/10.1007/978-3-642-31715-6_33.

[4] C. Alcalde, A. Burusco, R. Fuentes-González, et al. “The use of linguistic variables and fuzzy propositions in the L-Fuzzy concept theory”. In: Computers & Mathematics with Applications 62.8 (Oct. 2011), p. 3111–3122. ISSN: 0898-1221. DOI: 10.1016/j.camwa.2011.08.024. URL: http://dx.doi.org/10.1016/j.camwa.2011.08.024.

[5] 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.

[6] R. Belohlavek. “Relational Data,Formal Concept Analysis, and Graded Attributes”. In: Handbook of Research on Fuzzy Information Processing in Databases. IGI Global, 2008, p. 462–489. DOI: 10.4018/978-1-59904-853-6.ch018. URL: http://dx.doi.org/10.4018/978-1-59904-853-6.ch018.

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[8] P. Butka, J. Pócs, and J. Pócsová. “On equivalence of conceptual scaling and generalized one-sided concept lattices”. In: Information Sciences 259 (Feb. 2014), p. 57–70. ISSN: 0020-0255. DOI: 10.1016/j.ins.2013.08.047. URL: http://dx.doi.org/10.1016/j.ins.2013.08.047.

[9] P. Butka, J. Pócs, and J. Pócsová. “Representation of Fuzzy Concept Lattices in the Framework of Classical FCA”. In: Journal of Applied Mathematics 2013 (2013), p. 1–7. ISSN: 1687-0042. DOI: 10.1155/2013/236725. URL: http://dx.doi.org/10.1155/2013/236725.

[10] P. Butka, J. Pocsova, and J. Pocs. “Bisection-based merging algorithm for creation of one-sided concept lattices”. In: 2014 IEEE 12th International Symposium on Applied Machine Intelligence and Informatics (SAMI). IEEE, Jan. 2014, p. 103–108. DOI: 10.1109/sami.2014.6822386. URL: http://dx.doi.org/10.1109/sami.2014.6822386.

[11] H. Lai and L. Shen. “Multi-adjoint concept lattices via quantaloid-enriched categories”. In: Fuzzy Sets and Systems 405 (Feb. 2021), p. 74–87. ISSN: 0165-0114. DOI: 10.1016/j.fss.2020.03.007. URL: http://dx.doi.org/10.1016/j.fss.2020.03.007.

[12] L. Li and J. Zhang. “Attribute reduction in fuzzy concept lattices based on the T implication”. In: Knowledge-Based Systems 23.6 (Aug. 2010), p. 497–503. ISSN: 0950-7051. DOI: 10.1016/j.knosys.2010.03.006. URL: http://dx.doi.org/10.1016/j.knosys.2010.03.006.

[13] J. Medina and M. Ojeda-Aciego. “Multi-adjoint t-concept lattices”. In: Information Sciences 180.5 (Mar. 2010), p. 712–725. ISSN: 0020-0255. DOI: 10.1016/j.ins.2009.11.018. URL: http://dx.doi.org/10.1016/j.ins.2009.11.018.

[14] J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. “Formal concept analysis via multi-adjoint concept lattices”. In: Fuzzy Sets and Systems 160.2 (Jan. 2009), p. 130–144. ISSN: 0165-0114. DOI: 10.1016/j.fss.2008.05.004. URL: http://dx.doi.org/10.1016/j.fss.2008.05.004.

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[17] J. Pócs. “Note on generating fuzzy concept lattices via Galois connections”. In: Information Sciences 185.1 (Feb. 2012), p. 128–136. ISSN: 0020-0255. DOI: 10.1016/j.ins.2011.09.021. URL: http://dx.doi.org/10.1016/j.ins.2011.09.021.

[18] J. Poelmans, D. I. Ignatov, S. O. Kuznetsov, et al. “Fuzzy and rough formal concept analysis: a survey”. In: International Journal of General Systems 43.2 (Jan. 2014), p. 105–134. ISSN: 1563-5104. DOI: 10.1080/03081079.2013.862377. URL: http://dx.doi.org/10.1080/03081079.2013.862377.

[19] J. Poelmans, S. O. Kuznetsov, D. I. Ignatov, et al. “Formal Concept Analysis in knowledge processing: A survey on models and techniques”. In: Expert Systems with Applications 40.16 (Nov. 2013), p. 6601–6623. ISSN: 0957-4174. DOI: 10.1016/j.eswa.2013.05.007. URL: http://dx.doi.org/10.1016/j.eswa.2013.05.007.

[20] L. Wang, X. Liu, and J. Cao. “A new algebraic structure for formal concept analysis”. In: Information Sciences 180.24 (Dec. 2010), p. 4865–4876. ISSN: 0020-0255. DOI: 10.1016/j.ins.2010.08.020. URL: http://dx.doi.org/10.1016/j.ins.2010.08.020.

[21] W. Yao, S. Han, and R. Wang. “Lattice-theoretic contexts and their concept lattices via Galois ideals”. In: Information Sciences 339 (Apr. 2016), p. 1–18. ISSN: 0020-0255. DOI: 10.1016/j.ins.2015.12.028. URL: http://dx.doi.org/10.1016/j.ins.2015.12.028.

[22] Y. Zhai and D. Li. “Knowledge structure preserving fuzzy attribute reduction in fuzzy formal context”. In: International Journal of Approximate Reasoning 115 (Dec. 2019), p. 209–220. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2019.09.012. URL: http://dx.doi.org/10.1016/j.ijar.2019.09.012.