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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.
Keywords
Left-compatibility, Right-compatibility, Clone relation, Order relation, Fuzzy equivalence relation, Fuzzy tolerance relation

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Citation

Please use this url to cite or link to this publication:

Chicago
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.
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.
Vancouver
1.
Zedam L, Bouremel H, De Baets B. Left- and right-compatibility of order relations and fuzzy tolerance relations. Fuzzy Sets and Systems. Elsevier BV; 2019;360:65–81.
MLA
Zedam, Lemnaouar, Hassane Bouremel, and Bernard De Baets. “Left- and Right-compatibility of Order Relations and Fuzzy Tolerance Relations.” Fuzzy Sets and Systems 360 (2019): 65–81. Print.
@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.},
  author       = {Zedam, Lemnaouar and Bouremel, Hassane and De Baets, Bernard},
  issn         = {0165-0114},
  journal      = {Fuzzy Sets and Systems},
  pages        = {65--81},
  publisher    = {Elsevier BV},
  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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