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Traces of ternary relations

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Abstract
In this paper, we generalize the notion of traces of a binary relation to the setting of ternary relations. With a given ternary relation, we associate three binary relations: its left, middle and right trace. As in the binary case, these traces facilitate the study and characterization of properties of a ternary relation. Interestingly, the traces themselves turn out to be the greatest solutions of relational inequalities associated with newly introduced compositions of a ternary relation with a binary relation (and vice versa).
Keywords
Binary relation, ternary relation, traces, relational compositions, TRIADIC CONCEPT LATTICES, CYCLICALLY ORDERED SETS, FORMAL CONCEPT ANALYSIS, N-ARY RELATIONS, FUZZY RELATIONS, RANKING RULES, ALGEBRAS, RATIONALIZATION, BETWEENNESS, HYPERGROUPS

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MLA
Zedam, Lemnaouar, et al. “Traces of Ternary Relations.” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol. 47, no. 4, 2018, pp. 350–73, doi:10.1080/03081079.2018.1446433.
APA
Zedam, L., Barkat, O., & De Baets, B. (2018). Traces of ternary relations. INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 47(4), 350–373. https://doi.org/10.1080/03081079.2018.1446433
Chicago author-date
Zedam, Lemnaouar, Omar Barkat, and Bernard De Baets. 2018. “Traces of Ternary Relations.” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 47 (4): 350–73. https://doi.org/10.1080/03081079.2018.1446433.
Chicago author-date (all authors)
Zedam, Lemnaouar, Omar Barkat, and Bernard De Baets. 2018. “Traces of Ternary Relations.” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 47 (4): 350–373. doi:10.1080/03081079.2018.1446433.
Vancouver
1.
Zedam L, Barkat O, De Baets B. Traces of ternary relations. INTERNATIONAL JOURNAL OF GENERAL SYSTEMS. 2018;47(4):350–73.
IEEE
[1]
L. Zedam, O. Barkat, and B. De Baets, “Traces of ternary relations,” INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol. 47, no. 4, pp. 350–373, 2018.
@article{8578988,
  abstract     = {{In this paper, we generalize the notion of traces of a binary relation to the setting of ternary relations. With a given ternary relation, we associate three binary relations: its left, middle and right trace. As in the binary case, these traces facilitate the study and characterization of properties of a ternary relation. Interestingly, the traces themselves turn out to be the greatest solutions of relational inequalities associated with newly introduced compositions of a ternary relation with a binary relation (and vice versa).}},
  author       = {{Zedam, Lemnaouar and Barkat, Omar and De Baets, Bernard}},
  issn         = {{0308-1079}},
  journal      = {{INTERNATIONAL JOURNAL OF GENERAL SYSTEMS}},
  keywords     = {{Binary relation,ternary relation,traces,relational compositions,TRIADIC CONCEPT LATTICES,CYCLICALLY ORDERED SETS,FORMAL CONCEPT ANALYSIS,N-ARY RELATIONS,FUZZY RELATIONS,RANKING RULES,ALGEBRAS,RATIONALIZATION,BETWEENNESS,HYPERGROUPS}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{350--373}},
  title        = {{Traces of ternary relations}},
  url          = {{http://dx.doi.org/10.1080/03081079.2018.1446433}},
  volume       = {{47}},
  year         = {{2018}},
}

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