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Clonal sets of a binary relation

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Abstract
In a recent paper, we have introduced the notion of clone relation of a given binary relation. Intuitively, two elements are said to be clones if they are related in the same way w.r.t. every other element. In this paper, we generalize this notion from pairs of elements to sets of elements of any cardinality, resulting in the introduction of clonal sets. We investigate the most important properties of clonal sets, paying particular attention to the introduction of the clonal closure operator, to the analysis of the (lattice) structure of the set of clonal sets and to a distance metric expressing how close two elements are to being clones.
Keywords
Clone relation, clonal set, clonal closure, clonal lattice, clonal distance metric, FUZZY, COMPATIBILITY, INDEPENDENCE, LATTICES

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MLA
Zedam, Lemnaouar, et al. “Clonal Sets of a Binary Relation.” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol. 47, no. 4, 2018, pp. 329–49, doi:10.1080/03081079.2018.1445738.
APA
Zedam, L., Perez Fernandez, R., Bouremel, H., & De Baets, B. (2018). Clonal sets of a binary relation. INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 47(4), 329–349. https://doi.org/10.1080/03081079.2018.1445738
Chicago author-date
Zedam, Lemnaouar, Raul Perez Fernandez, Hassane Bouremel, and Bernard De Baets. 2018. “Clonal Sets of a Binary Relation.” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 47 (4): 329–49. https://doi.org/10.1080/03081079.2018.1445738.
Chicago author-date (all authors)
Zedam, Lemnaouar, Raul Perez Fernandez, Hassane Bouremel, and Bernard De Baets. 2018. “Clonal Sets of a Binary Relation.” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 47 (4): 329–349. doi:10.1080/03081079.2018.1445738.
Vancouver
1.
Zedam L, Perez Fernandez R, Bouremel H, De Baets B. Clonal sets of a binary relation. INTERNATIONAL JOURNAL OF GENERAL SYSTEMS. 2018;47(4):329–49.
IEEE
[1]
L. Zedam, R. Perez Fernandez, H. Bouremel, and B. De Baets, “Clonal sets of a binary relation,” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol. 47, no. 4, pp. 329–349, 2018.
@article{8578987,
  abstract     = {{In a recent paper, we have introduced the notion of clone relation of a given binary relation. Intuitively, two elements are said to be clones if they are related in the same way w.r.t. every other element. In this paper, we generalize this notion from pairs of elements to sets of elements of any cardinality, resulting in the introduction of clonal sets. We investigate the most important properties of clonal sets, paying particular attention to the introduction of the clonal closure operator, to the analysis of the (lattice) structure of the set of clonal sets and to a distance metric expressing how close two elements are to being clones.}},
  author       = {{Zedam, Lemnaouar and Perez Fernandez, Raul and Bouremel, Hassane and De Baets, Bernard}},
  issn         = {{0308-1079}},
  journal      = {{INTERNATIONAL JOURNAL OF GENERAL SYSTEMS}},
  keywords     = {{Clone relation,clonal set,clonal closure,clonal lattice,clonal distance metric,FUZZY,COMPATIBILITY,INDEPENDENCE,LATTICES}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{329--349}},
  title        = {{Clonal sets of a binary relation}},
  url          = {{http://doi.org/10.1080/03081079.2018.1445738}},
  volume       = {{47}},
  year         = {{2018}},
}

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