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On the degree of asymmetry of a quasi-copula with respect to a curve

Bernard De Baets (UGent) , Hans De Meyer (UGent) and Tarad Jwaid (UGent)
(2019) Fuzzy Sets and Systems. 354. p.84-103
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Abstract
The geometrical interpretation of symmetry of a function on the unit square is that it takes the same value in mirror images w.r.t. the main diagonal. Here, this concept is generalized by considering the reflection w.r.t. a curve representing the graph of an automorphism of the unit interval. A function on the unit square that takes the same value in mirror images w.r.t. such a curve is called symmetric w.r.t. that curve. Moreover, a measure is proposed for quantifying to what extent a (quasi-)copula can be regarded as being asymmetric w.r.t. a given curve. The major part of the paper is concerned with establishing lower and upper bounds on this degree of asymmetry. Finally, it is shown that these bounds are sharp within the class of copulas.
Keywords
Copula Curvilinear section Degree of asymmetry Quasi-copula

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Citation

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

Chicago
De Baets, Bernard, Hans De Meyer, and Tarad Jwaid. 2019. “On the Degree of Asymmetry of a Quasi-copula with Respect to a Curve.” Fuzzy Sets and Systems 354: 84–103.
APA
De Baets, B., De Meyer, H., & Jwaid, T. (2019). On the degree of asymmetry of a quasi-copula with respect to a curve. Fuzzy Sets and Systems, 354, 84–103.
Vancouver
1.
De Baets B, De Meyer H, Jwaid T. On the degree of asymmetry of a quasi-copula with respect to a curve. Fuzzy Sets and Systems. Elsevier BV; 2019;354:84–103.
MLA
De Baets, Bernard, Hans De Meyer, and Tarad Jwaid. “On the Degree of Asymmetry of a Quasi-copula with Respect to a Curve.” Fuzzy Sets and Systems 354 (2019): 84–103. Print.
@article{8607547,
  abstract     = {The geometrical interpretation of symmetry of a function on the unit square is that it takes the same value in mirror images w.r.t. the main diagonal. Here, this concept is generalized by considering the reflection w.r.t. a curve representing the graph of an automorphism of the unit interval. A function on the unit square that takes the same value in mirror images w.r.t. such a curve is called symmetric w.r.t. that curve. Moreover, a measure is proposed for quantifying to what extent a (quasi-)copula can be regarded as being asymmetric w.r.t. a given curve. The major part of the paper is concerned with establishing lower and upper bounds on this degree of asymmetry. Finally, it is shown that these bounds are sharp within the class of copulas.},
  author       = {De Baets, Bernard and De Meyer, Hans and Jwaid, Tarad},
  issn         = {0165-0114},
  journal      = {Fuzzy Sets and Systems},
  pages        = {84--103},
  publisher    = {Elsevier BV},
  title        = {On the degree of asymmetry of a quasi-copula with respect to a curve},
  url          = {http://dx.doi.org/10.1016/j.fss.2018.05.002},
  volume       = {354},
  year         = {2019},
}

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