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Left- and right-compatibility of order relations and fuzzy tolerance relations

(2019) FUZZY SETS AND SYSTEMS. 360. p.65-81
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Abstract
In a recent paper, De Baets et al. have studied the compatibility of a(n) (strict) order relation with a fuzzy relation, and have characterized the fuzzy tolerance (and, in particular, fuzzy equivalence) relations that a given strict order relation is compatible with. We extend this study by considering the left- and right-compatibility of a(n) (strict) order relation with a fuzzy tolerance relation and vice versa. We characterize the fuzzy tolerance relations that are compatible with a given (strict) order relation. Conversely, we provide a representation of the fuzzy tolerance relations that a given strict order relation is left- or right-compatible with. Specific attention is paid to the case of fuzzy equivalence relations. We conclude by pointing out that the representation theorems in the above-mentioned paper need some minor rectification. (C) 2018 Elsevier B.V. All rights reserved.
Keywords
Left-compatibility, Right-compatibility, Clone relation, Order relation, Fuzzy equivalence relation, Fuzzy tolerance relation, VALUED EQUIVALENCE-RELATIONS, LATTICES, ALGEBRA

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MLA
Zedam, Lemnaouar, et al. “Left- and Right-Compatibility of Order Relations and Fuzzy Tolerance Relations.” FUZZY SETS AND SYSTEMS, vol. 360, 2019, pp. 65–81, doi:10.1016/j.fss.2018.05.021.
APA
Zedam, L., Bouremel, H., & De Baets, B. (2019). Left- and right-compatibility of order relations and fuzzy tolerance relations. FUZZY SETS AND SYSTEMS, 360, 65–81. https://doi.org/10.1016/j.fss.2018.05.021
Chicago author-date
Zedam, Lemnaouar, Hassane Bouremel, and Bernard De Baets. 2019. “Left- and Right-Compatibility of Order Relations and Fuzzy Tolerance Relations.” FUZZY SETS AND SYSTEMS 360: 65–81. https://doi.org/10.1016/j.fss.2018.05.021.
Chicago author-date (all authors)
Zedam, Lemnaouar, Hassane Bouremel, and Bernard De Baets. 2019. “Left- and Right-Compatibility of Order Relations and Fuzzy Tolerance Relations.” FUZZY SETS AND SYSTEMS 360: 65–81. doi:10.1016/j.fss.2018.05.021.
Vancouver
1.
Zedam L, Bouremel H, De Baets B. Left- and right-compatibility of order relations and fuzzy tolerance relations. FUZZY SETS AND SYSTEMS. 2019;360:65–81.
IEEE
[1]
L. Zedam, H. Bouremel, and B. De Baets, “Left- and right-compatibility of order relations and fuzzy tolerance relations,” FUZZY SETS AND SYSTEMS, vol. 360, pp. 65–81, 2019.
@article{8607568,
  abstract     = {{In a recent paper, De Baets et al. have studied the compatibility of a(n) (strict) order relation with a fuzzy relation, and have characterized the fuzzy tolerance (and, in particular, fuzzy equivalence) relations that a given strict order relation is compatible with. We extend this study by considering the left- and right-compatibility of a(n) (strict) order relation with a fuzzy tolerance relation and vice versa. We characterize the fuzzy tolerance relations that are compatible with a given (strict) order relation. Conversely, we provide a representation of the fuzzy tolerance relations that a given strict order relation is left- or right-compatible with. Specific attention is paid to the case of fuzzy equivalence relations. We conclude by pointing out that the representation theorems in the above-mentioned paper need some minor rectification. (C) 2018 Elsevier B.V. All rights reserved.}},
  author       = {{Zedam, Lemnaouar and Bouremel, Hassane and De Baets, Bernard}},
  issn         = {{0165-0114}},
  journal      = {{FUZZY SETS AND SYSTEMS}},
  keywords     = {{Left-compatibility,Right-compatibility,Clone relation,Order relation,Fuzzy equivalence relation,Fuzzy tolerance relation,VALUED EQUIVALENCE-RELATIONS,LATTICES,ALGEBRA}},
  language     = {{eng}},
  pages        = {{65--81}},
  title        = {{Left- and right-compatibility of order relations and fuzzy tolerance relations}},
  url          = {{http://dx.doi.org/10.1016/j.fss.2018.05.021}},
  volume       = {{360}},
  year         = {{2019}},
}

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