On homogeneous -bonds and heterogeneous -bonds

 

Abstract

In this paper, we deal with suitable generalizations of the notion of bond between contexts, as part of the research area of Formal Concept Analysis. We study different generalizations of the notion of bond within the L-fuzzy setting. Specifically, given a formal context, there are three prototypical pairs of concept-forming operators, and this immediately leads to three possible versions of the notion of bond (so-called homogeneous bond wrt certain pair of concept-forming operators). The first results show a close correspondence between a homogeneous bond between two contexts and certain special types of mappings between the sets of extents (or intents) of the corresponding concept lattices. Later, we introduce the so-called heterogeneous bonds (considering simultaneously two types of concept-forming operators) and generalize the previous relationship to mappings between the sets of extents (or intents) of the corresponding concept lattices.

Citation

Please, cite this work as:

[KO16] J. Konecny and M. Ojeda-Aciego. “On homogeneous L-bonds and heterogeneous L-bonds”. In: Int. J. Gen. Syst. 45.2 (2016), pp. 160-186. DOI: 10.1080/03081079.2015.1072926. URL: https://doi.org/10.1080/03081079.2015.1072926.

BibTeX

@Article{Konecny2016,
     author = {Jan Konecny and Manuel Ojeda-Aciego},
     journal = {Int. J. Gen. Syst.},
     title = {On homogeneous -bonds and heterogeneous -bonds},
     year = {2016},
     number = {2},
     pages = {160–186},
     volume = {45},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/journals/ijgs/KonecnyO16.bib},
     doi = {10.1080/03081079.2015.1072926},
     timestamp = {Thu, 20 Aug 2020 01:00:00 +0200},
     url = {https://doi.org/10.1080/03081079.2015.1072926},
}

Bibliometric data

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

6

CITATIONS

6 Total citations

1 Recent citation

3.58 Field Citation Ratio

n/a Relative Citation Ratio

• Citations
• CrossRef - Citation Indexes: 2
• Scopus - Citation Indexes: 6

• Captures
• Mendeley - Readers: 4

-

see details

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] L. Antoni, S. Krajči, and O. Krídlo. “On stability of fuzzy formal concepts over randomized one-sided formal context”. In: Fuzzy Sets and Systems 333 (Feb. 2018), p. 36–53. ISSN: 0165-0114. DOI: 10.1016/j.fss.2017.04.006. URL: http://dx.doi.org/10.1016/j.fss.2017.04.006.

[2] R. G. Aragón, J. Medina, and S. Molina-Ruiz. “The Notion of Bond in the Multi-adjoint Concept Lattice Framework”. In: Advances in Artificial Intelligence. Springer Nature Switzerland, 2024, p. 243–253. ISBN: 9783031627996. DOI: 10.1007/978-3-031-62799-6_25. URL: http://dx.doi.org/10.1007/978-3-031-62799-6_25.

[3] J. Konecny and M. Krupka. “Block relations in formal fuzzy concept analysis”. In: International Journal of Approximate Reasoning 73 (Jun. 2016), p. 27–55. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2016.02.004. URL: http://dx.doi.org/10.1016/j.ijar.2016.02.004.

[4] O. Krídlo, Ľ. Antoni, and S. Krajči. “Selection of appropriate bonds between L-fuzzy formal contexts for recommendation tasks”. In: Information Sciences 606 (Aug. 2022), p. 21–37. ISSN: 0020-0255. DOI: 10.1016/j.ins.2022.05.047. URL: http://dx.doi.org/10.1016/j.ins.2022.05.047.

[5] O. Krídlo, D. López-Rodríguez, L. Antoni, et al. “Connecting concept lattices with bonds induced by external information”. In: Information Sciences 648 (Nov. 2023), p. 119498. ISSN: 0020-0255. DOI: 10.1016/j.ins.2023.119498. URL: http://dx.doi.org/10.1016/j.ins.2023.119498.

[6] J. Pócs and J. Pócsová. “On Bonds for Generalized One-Sided Concept Lattices”. In: Mathematics 9.3 (Jan. 2021), p. 211. ISSN: 2227-7390. DOI: 10.3390/math9030211. URL: http://dx.doi.org/10.3390/math9030211.