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On the lattice structure of the set of supermodular quasi-copulas

(2019) Fuzzy Sets and Systems. 354. p.74-83
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Abstract
We study the relationship between the poset of supermodular n-quasi-copulas and the posets of n-quasi-copulas and n-copulas. It is known that, for , the poset of n-quasi-copulas is not order-isomorphic to the Dedekind–MacNeille completion of the poset of n-copulas. We complement the latter result by showing that, for , the structure of the poset of n-quasi-copulas is more closely related to that of the poset of supermodular n-quasi-copulas than that of the poset of n-copulas.
Keywords
n-Quasi-copula n-Copula Supermodularity Lattice

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Citation

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Chicago
Arias García, José De Jesús, and Bernard De Baets. 2019. “On the Lattice Structure of the Set of Supermodular Quasi-copulas.” Fuzzy Sets and Systems 354: 74–83.
APA
Arias García, J. D. J., & De Baets, B. (2019). On the lattice structure of the set of supermodular quasi-copulas. Fuzzy Sets and Systems, 354, 74–83.
Vancouver
1.
Arias García JDJ, De Baets B. On the lattice structure of the set of supermodular quasi-copulas. Fuzzy Sets and Systems. Elsevier BV; 2019;354:74–83.
MLA
Arias García, José De Jesús, and Bernard De Baets. “On the Lattice Structure of the Set of Supermodular Quasi-copulas.” Fuzzy Sets and Systems 354 (2019): 74–83. Print.
@article{8607542,
  abstract     = {We study the relationship between the poset of supermodular n-quasi-copulas and the posets of n-quasi-copulas and n-copulas. It is known that, for , the poset of n-quasi-copulas is not order-isomorphic to the Dedekind--MacNeille completion of the poset of n-copulas. We complement the latter result by showing that, for , the structure of the poset of n-quasi-copulas is more closely related to that of the poset of supermodular n-quasi-copulas than that of the poset of n-copulas.},
  author       = {Arias Garc{\'i}a, Jos{\'e} De Jes{\'u}s and De Baets, Bernard},
  issn         = {0165-0114},
  journal      = {Fuzzy Sets and Systems},
  pages        = {74--83},
  publisher    = {Elsevier BV},
  title        = {On the lattice structure of the set of supermodular quasi-copulas},
  url          = {http://dx.doi.org/10.1016/j.fss.2018.03.013},
  volume       = {354},
  year         = {2019},
}

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