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Closures and openings of ternary relations

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Abstract
In this paper, we study the problem of closing or opening a ternary relation with respect to various relational properties, with a focus on the many transitivity properties that have been proposed for ternary relations over the past years. In particular, we consider the transitivity properties corresponding to the six relational compositions of ternary relations recently introduced by Bakri et al., making a careful distinction between the four associative ones and the two non-associative ones.
Keywords
Ternary relation, relational composition, transitivity, closure, opening

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MLA
Zedam, Lemnaouar, et al. “Closures and Openings of Ternary Relations.” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol. 49, no. 7, 2020, pp. 760–84, doi:10.1080/03081079.2020.1832486.
APA
Zedam, L., Bakri, N., & De Baets, B. (2020). Closures and openings of ternary relations. INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 49(7), 760–784. https://doi.org/10.1080/03081079.2020.1832486
Chicago author-date
Zedam, Lemnaouar, Nourelhouda Bakri, and Bernard De Baets. 2020. “Closures and Openings of Ternary Relations.” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 49 (7): 760–84. https://doi.org/10.1080/03081079.2020.1832486.
Chicago author-date (all authors)
Zedam, Lemnaouar, Nourelhouda Bakri, and Bernard De Baets. 2020. “Closures and Openings of Ternary Relations.” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 49 (7): 760–784. doi:10.1080/03081079.2020.1832486.
Vancouver
1.
Zedam L, Bakri N, De Baets B. Closures and openings of ternary relations. INTERNATIONAL JOURNAL OF GENERAL SYSTEMS. 2020;49(7):760–84.
IEEE
[1]
L. Zedam, N. Bakri, and B. De Baets, “Closures and openings of ternary relations,” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol. 49, no. 7, pp. 760–784, 2020.
@article{8680112,
  abstract     = {In this paper, we study the problem of closing or opening a ternary relation with respect to various relational properties, with a focus on the many transitivity properties that have been proposed for ternary relations over the past years. In particular, we consider the transitivity properties corresponding to the six relational compositions of ternary relations recently introduced by Bakri et al., making a careful distinction between the four associative ones and the two non-associative ones.},
  author       = {Zedam, Lemnaouar and Bakri, Nourelhouda and De Baets, Bernard},
  issn         = {0308-1079},
  journal      = {INTERNATIONAL JOURNAL OF GENERAL SYSTEMS},
  keywords     = {Ternary relation,relational composition,transitivity,closure,opening},
  language     = {eng},
  number       = {7},
  pages        = {760--784},
  title        = {Closures and openings of ternary relations},
  url          = {http://dx.doi.org/10.1080/03081079.2020.1832486},
  volume       = {49},
  year         = {2020},
}

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