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An overview of the fuzzy axiomatic systems and characterizations proposed at Ghent University

Etienne Kerre (UGent) , Lynn D'eer (UGent) and Bart Van Gasse (UGent)
(2016) AXIOMS. 5(2).
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Abstract
During the past 40 years of fuzzy research at the Fuzziness and Uncertainty Modeling research unit of Ghent University several axiomatic systems and characterizations have been introduced. In this paper we highlight some of them. The main purpose of this paper consists of an invitation to continue research on these first attempts to axiomatize important concepts and systems in fuzzy set theory. Currently, these attempts are spread over many journals; with this paper they are now collected in a neat overview. In the literature, many axiom systems have been introduced, but as far as we know the axiomatic system of Huntington concerning a Boolean algebra has been the only one where the axioms have been proven independent. Another line of further research could be with respect to the simplification of these systems, in discovering redundancies between the axioms.
Keywords
fuzzy topology, fuzzy set, fuzzy preference structure

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MLA
Kerre, Etienne, et al. “An Overview of the Fuzzy Axiomatic Systems and Characterizations Proposed at Ghent University.” AXIOMS, edited by Angel Garrido and Urszula Wybraniec-Skardowska, vol. 5, no. 2, 2016, doi:10.3390/axioms5020017.
APA
Kerre, E., D’eer, L., & Van Gasse, B. (2016). An overview of the fuzzy axiomatic systems and characterizations proposed at Ghent University. AXIOMS, 5(2). https://doi.org/10.3390/axioms5020017
Chicago author-date
Kerre, Etienne, Lynn D’eer, and Bart Van Gasse. 2016. “An Overview of the Fuzzy Axiomatic Systems and Characterizations Proposed at Ghent University.” Edited by Angel Garrido and Urszula Wybraniec-Skardowska. AXIOMS 5 (2). https://doi.org/10.3390/axioms5020017.
Chicago author-date (all authors)
Kerre, Etienne, Lynn D’eer, and Bart Van Gasse. 2016. “An Overview of the Fuzzy Axiomatic Systems and Characterizations Proposed at Ghent University.” Ed by. Angel Garrido and Urszula Wybraniec-Skardowska. AXIOMS 5 (2). doi:10.3390/axioms5020017.
Vancouver
1.
Kerre E, D’eer L, Van Gasse B. An overview of the fuzzy axiomatic systems and characterizations proposed at Ghent University. Garrido A, Wybraniec-Skardowska U, editors. AXIOMS. 2016;5(2).
IEEE
[1]
E. Kerre, L. D’eer, and B. Van Gasse, “An overview of the fuzzy axiomatic systems and characterizations proposed at Ghent University,” AXIOMS, vol. 5, no. 2, 2016.
@article{7252922,
  abstract     = {{During the past 40 years of fuzzy research at the Fuzziness and Uncertainty Modeling research unit of Ghent University several axiomatic systems and characterizations have been introduced. In this paper we highlight some of them. The main purpose of this paper consists of an invitation to continue research on these first attempts to axiomatize important concepts and systems in fuzzy set theory. Currently, these attempts are spread over many journals; with this paper they are now collected in a neat overview. In the literature, many axiom systems have been introduced, but as far as we know the axiomatic system of Huntington concerning a Boolean algebra has been the only one where the axioms have been proven independent. Another line of further research could be with respect to the simplification of these systems, in discovering redundancies between the axioms.}},
  articleno    = {{17}},
  author       = {{Kerre, Etienne and D'eer, Lynn and Van Gasse, Bart}},
  editor       = {{Garrido, Angel and Wybraniec-Skardowska, Urszula}},
  issn         = {{2075-1680}},
  journal      = {{AXIOMS}},
  keywords     = {{fuzzy topology,fuzzy set,fuzzy preference structure}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{13}},
  title        = {{An overview of the fuzzy axiomatic systems and characterizations proposed at Ghent University}},
  url          = {{http://doi.org/10.3390/axioms5020017}},
  volume       = {{5}},
  year         = {{2016}},
}
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