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On the compatibility of a ternary relation with a binary fuzzy relation

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Abstract
Recently, De Baets et al. have characterized the fuzzy tolerance relations that a given strict order relation is compatible with. In general, the compatibility of a strict order relation with a binary fuzzy relation guarantees also the compatibility of its associated betweenness relation with that binary fuzzy relation. In this paper, we study the compatibility of an arbitrary ternary relation with a binary fuzzy relation. We prove that this compatibility can be expressed in terms of inclusions of the binary fuzzy relation in the traces of the given ternary relation.
Keywords
Ternary relation, binary fuzzy relation, traces of a ternary relation, compatibility, VALUED EQUIVALENCE-RELATIONS, LATTICES, ALGEBRA

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MLA
Barkat, Omar, et al. “On the Compatibility of a Ternary Relation with a Binary Fuzzy Relation.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol. 27, no. 4, 2019, pp. 595–612.
APA
Barkat, O., Zedam, L., & De Baets, B. (2019). On the compatibility of a ternary relation with a binary fuzzy relation. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 27(4), 595–612.
Chicago author-date
Barkat, Omar, Lemnaouar Zedam, and Bernard De Baets. 2019. “On the Compatibility of a Ternary Relation with a Binary Fuzzy Relation.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 27 (4): 595–612.
Chicago author-date (all authors)
Barkat, Omar, Lemnaouar Zedam, and Bernard De Baets. 2019. “On the Compatibility of a Ternary Relation with a Binary Fuzzy Relation.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 27 (4): 595–612.
Vancouver
1.
Barkat O, Zedam L, De Baets B. On the compatibility of a ternary relation with a binary fuzzy relation. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS. 2019;27(4):595–612.
IEEE
[1]
O. Barkat, L. Zedam, and B. De Baets, “On the compatibility of a ternary relation with a binary fuzzy relation,” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol. 27, no. 4, pp. 595–612, 2019.
@article{8626851,
  abstract     = {Recently, De Baets et al. have characterized the fuzzy tolerance relations that a given strict order relation is compatible with. In general, the compatibility of a strict order relation with a binary fuzzy relation guarantees also the compatibility of its associated betweenness relation with that binary fuzzy relation. In this paper, we study the compatibility of an arbitrary ternary relation with a binary fuzzy relation. We prove that this compatibility can be expressed in terms of inclusions of the binary fuzzy relation in the traces of the given ternary relation.},
  author       = {Barkat, Omar and Zedam, Lemnaouar and De Baets, Bernard},
  issn         = {0218-4885},
  journal      = {INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS},
  keywords     = {Ternary relation,binary fuzzy relation,traces of a ternary relation,compatibility,VALUED EQUIVALENCE-RELATIONS,LATTICES,ALGEBRA},
  language     = {eng},
  number       = {4},
  pages        = {595--612},
  title        = {On the compatibility of a ternary relation with a binary fuzzy relation},
  url          = {http://dx.doi.org/10.1142/s0218488519500260},
  volume       = {27},
  year         = {2019},
}

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