Generalizations of lattices via non-deterministic operators

uncategorised

Authors

Javier Martínez

Gloria Gutiérrez

Inmaculada Perez de Guzmán

Pablo Cordero

Published

1 January 2005

Publication details

Discret. Math. vol. 295 (1-3), pages 107–141.

Links

Abstract

Citation

Please, cite this work as:

[Mar+05] J. Mart', G. Gutiérrez, I. P. de Guzmán, et al. “Generalizations of lattices via non-deterministic operators”. In: Discret. Math. 295.1-3 (2005), pp. 107-141. DOI: 10.1016/J.DISC.2004.08.043. URL: https://doi.org/10.1016/j.disc.2004.08.043.

BibTeX

@Article{Martinez2005,
     author = {Javier Mart'and Gloria Guti{’e}rrez and Inmaculada Perez {de Guzm{’a}n} and Pablo Cordero},
     journal = {Discret. Math.},
     title = {Generalizations of lattices via non-deterministic operators},
     year = {2005},
     number = {1-3},
     pages = {107–141},
     volume = {295},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/journals/dm/MartinezGGC05.bib},
     doi = {10.1016/J.DISC.2004.08.043},
     timestamp = {Tue, 29 Aug 2023 01:00:00 +0200},
     url = {https://doi.org/10.1016/j.disc.2004.08.043},
}

Bibliometric data

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

Citations
CrossRef - Citation Indexes: 15
Scopus - Citation Indexes: 25

Captures
Mendeley - Readers: 5

Cites

The following graph plots the number of cites received by this work from its publication, on a yearly basis.

Papers citing this work

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

[1] A. Belfodil, S. O. Kuznetsov, and M. Kaytoue. “On pattern setups and pattern multistructures”. In: International Journal of General Systems 49.8 (Sep. 2020), p. 785–818. ISSN: 1563-5104. DOI: 10.1080/03081079.2020.1806832. URL: http://dx.doi.org/10.1080/03081079.2020.1806832.

[2] I. P. Cabrera, P. Cordero, G. Gutiérrez, et al. “Congruence relations on some hyperstructures”. In: Annals of Mathematics and Artificial Intelligence 56.3–4 (Jul. 2009), p. 361–370. ISSN: 1573-7470. DOI: 10.1007/s10472-009-9146-5. URL: http://dx.doi.org/10.1007/s10472-009-9146-5.

[3] I. P. Cabrera, P. Cordero, G. Gutiérrez, et al. “Fuzzy congruence relations on nd-groupoids”. In: International Journal of Computer Mathematics 86.10–11 (Nov. 2009), p. 1684–1695. ISSN: 1029-0265. DOI: 10.1080/00207160902721797. URL: http://dx.doi.org/10.1080/00207160902721797.

[4] I. P. Cabrera, P. Cordero, and M. Ojeda-Aciego. “Non-deterministic Algebraic Structures for Soft Computing”. In: Advances in Computational Intelligence. Springer Berlin Heidelberg, 2011, p. 437–444. ISBN: 9783642214981. DOI: 10.1007/978-3-642-21498-1_55. URL: http://dx.doi.org/10.1007/978-3-642-21498-1_55.

[5] I. Cabrera, P. Cordero, G. Gutiérrez, et al. “A coalgebraic approach to non-determinism: Applications to multilattices”. In: Information Sciences 180.22 (Nov. 2010), p. 4323–4335. ISSN: 0020-0255. DOI: 10.1016/j.ins.2010.07.002. URL: http://dx.doi.org/10.1016/j.ins.2010.07.002.

[6] I. Cabrera, P. Cordero, G. Gutiérrez, et al. “Finitary coalgebraic multisemilattices and multilattices”. In: Applied Mathematics and Computation 219.1 (Sep. 2012), p. 31–44. ISSN: 0096-3003. DOI: 10.1016/j.amc.2011.10.081. URL: http://dx.doi.org/10.1016/j.amc.2011.10.081.

[7] I. Cabrera, P. Cordero, G. Gutiérrez, et al. “On residuation in multilattices: Filters, congruences, and homomorphisms”. In: Fuzzy Sets and Systems 234 (Jan. 2014), p. 1–21. ISSN: 0165-0114. DOI: 10.1016/j.fss.2013.04.002. URL: http://dx.doi.org/10.1016/j.fss.2013.04.002.

[8] P. Cordero, A. Mora, I. de Guzmán, et al. “Non-deterministic ideal operators: An adequate tool for formalization in Data Bases”. In: Discrete Applied Mathematics 156.6 (Mar. 2008), p. 911–923. ISSN: 0166-218X. DOI: 10.1016/j.dam.2007.02.014. URL: http://dx.doi.org/10.1016/j.dam.2007.02.014.

[9] L. É. Diékouam Fotso, C. P. Kengne, and D. C. Awouafack. “Fuzzy prime filter theorem in multilattices”. In: Fuzzy Sets and Systems 497 (Dec. 2024), p. 109148. ISSN: 0165-0114. DOI: 10.1016/j.fss.2024.109148. URL: http://dx.doi.org/10.1016/j.fss.2024.109148.

[10] L. N. Maffeu, C. Lele, J. B. Nganou, et al. “Multiplicative and implicative derivations on residuated multilattices”. In: Soft Computing 23.23 (Jun. 2019), p. 12199–12208. ISSN: 1433-7479. DOI: 10.1007/s00500-019-04184-z. URL: http://dx.doi.org/10.1007/s00500-019-04184-z.

[11] J. Medina-Moreno, M. Ojeda-Aciego, and J. Ruiz-Calviño. “Concept-Forming Operators on Multilattices”. In: Formal Concept Analysis. Springer Berlin Heidelberg, 2013, p. 203–215. ISBN: 9783642383175. DOI: 10.1007/978-3-642-38317-5_13. URL: http://dx.doi.org/10.1007/978-3-642-38317-5_13.

[12] J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. “Fuzzy logic programming via multilattices”. In: Fuzzy Sets and Systems 158.6 (Mar. 2007), p. 674–688. ISSN: 0165-0114. DOI: 10.1016/j.fss.2006.11.006. URL: http://dx.doi.org/10.1016/j.fss.2006.11.006.

[13] J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. “Multi-lattices as a Basis for Generalized Fuzzy Logic Programming”. In: Fuzzy Logic and Applications. Springer Berlin Heidelberg, 2006, p. 61–70. ISBN: 9783540325307. DOI: 10.1007/11676935_8. URL: http://dx.doi.org/10.1007/11676935_8.

[14] G. Nguepy Dongmo, B. B. Koguep Njionou, L. Kwuida, et al. “Multilattice as the set of truth values for fuzzy rough sets”. In: Journal of Applied Non-Classical Logics (Jul. 2024), p. 1–20. ISSN: 1958-5780. DOI: 10.1080/11663081.2024.2373016. URL: http://dx.doi.org/10.1080/11663081.2024.2373016.

[15] G. Nguepy Dongmo, B. B. Koguep Njionou, L. Kwuida, et al. “Rough Fuzzy Concept Analysis via Multilattice”. In: Rough Sets. Springer Nature Switzerland, 2023, p. 495–508. ISBN: 9783031509599. DOI: 10.1007/978-3-031-50959-9_34. URL: http://dx.doi.org/10.1007/978-3-031-50959-9_34.

[16] U. Straccia, M. Ojeda-Aciego, and C. V. Damásio. “On Fixed-Points of Multivalued Functions on Complete Lattices and Their Application to Generalized Logic Programs”. In: SIAM Journal on Computing 38.5 (Jan. 2009), p. 1881–1911. ISSN: 1095-7111. DOI: 10.1137/070695976. URL: http://dx.doi.org/10.1137/070695976.

[17] L. Zedam and B. De Baets. “Weaker forms of increasingness of binary operations and their role in the characterization of meet and join operations”. In: Fuzzy Sets and Systems 497 (Dec. 2024), p. 109116. ISSN: 0165-0114. DOI: 10.1016/j.fss.2024.109116. URL: http://dx.doi.org/10.1016/j.fss.2024.109116.