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On the Compatibility of a Ternary Relation with a Binary Fuzzy Relation

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Abstract
<jats:p> 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. </jats:p>
Keywords
Control and Systems Engineering, Software, Artificial Intelligence, Information Systems

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Chicago
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: 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, 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;27:595–612.
MLA
Barkat, Omar, Lemnaouar Zedam, and Bernard De Baets. “On the Compatibility of a Ternary Relation with a Binary Fuzzy Relation.” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 27 (2019): 595–612. Print.
@article{8626851,
  abstract     = {<jats:p> 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. </jats:p>},
  author       = {Barkat, Omar and Zedam, Lemnaouar and De Baets, Bernard},
  issn         = {0218-4885},
  journal      = {International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems},
  keywords     = {Control and Systems Engineering,Software,Artificial Intelligence,Information Systems},
  language     = {eng},
  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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