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Compatibility of fuzzy relations

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Abstract
The notion of extensionality, introduced by Hohle and Blanchard, and the notion of compatibility, as coined by Belohlavek, of a fuzzy relation with respect to a fuzzy equality are trivially equivalent. Here, this compatibility property is dissected into left and right compatibility, mimicking the original twofold definition of extensionality, and studied in detail in the context of arbitrary fuzzy relations. Relying on the notions of left and right traces of a fuzzy relation, it is shown that compatibility can be characterized in terms of inclusions, shedding another light on the matter.
Keywords
PREFERENCE STRUCTURES, SIMILARITY RELATIONS, REPRESENTATIONS, CONSTRUCTIONS, TRANSITIVITY, ORDERINGS, OPERATORS, LATTICES, ALGEBRA, TRACES

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Citation

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

MLA
Kheniche, Azzedine, Bernard De Baets, and Lemnaouar Zedam. “Compatibility of Fuzzy Relations.” INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS 31.3 (2016): 240–256. Print.
APA
Kheniche, A., De Baets, B., & Zedam, L. (2016). Compatibility of fuzzy relations. INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, 31(3), 240–256.
Chicago author-date
Kheniche, Azzedine, Bernard De Baets, and Lemnaouar Zedam. 2016. “Compatibility of Fuzzy Relations.” International Journal of Intelligent Systems 31 (3): 240–256.
Chicago author-date (all authors)
Kheniche, Azzedine, Bernard De Baets, and Lemnaouar Zedam. 2016. “Compatibility of Fuzzy Relations.” International Journal of Intelligent Systems 31 (3): 240–256.
Vancouver
1.
Kheniche A, De Baets B, Zedam L. Compatibility of fuzzy relations. INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS. 2016;31(3):240–56.
IEEE
[1]
A. Kheniche, B. De Baets, and L. Zedam, “Compatibility of fuzzy relations,” INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, vol. 31, no. 3, pp. 240–256, 2016.
@article{7167146,
  abstract     = {The notion of extensionality, introduced by Hohle and Blanchard, and the notion of compatibility, as coined by Belohlavek, of a fuzzy relation with respect to a fuzzy equality are trivially equivalent. Here, this compatibility property is dissected into left and right compatibility, mimicking the original twofold definition of extensionality, and studied in detail in the context of arbitrary fuzzy relations. Relying on the notions of left and right traces of a fuzzy relation, it is shown that compatibility can be characterized in terms of inclusions, shedding another light on the matter.},
  author       = {Kheniche, Azzedine and De Baets, Bernard and Zedam, Lemnaouar},
  issn         = {0884-8173},
  journal      = {INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS},
  keywords     = {PREFERENCE STRUCTURES,SIMILARITY RELATIONS,REPRESENTATIONS,CONSTRUCTIONS,TRANSITIVITY,ORDERINGS,OPERATORS,LATTICES,ALGEBRA,TRACES},
  language     = {eng},
  number       = {3},
  pages        = {240--256},
  title        = {Compatibility of fuzzy relations},
  url          = {http://dx.doi.org/10.1002/int.21783},
  volume       = {31},
  year         = {2016},
}

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