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Axioms 2016, 5(2), 17; doi:10.3390/axioms5020017

An Overview of the Fuzzy Axiomatic Systems and Characterizations Proposed at Ghent University

Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Building S9 (second floor), Krijgslaan 281, 9000 Ghent, Belgium
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Academic Editor: Humberto Bustince
Received: 17 March 2016 / Revised: 20 May 2016 / Accepted: 31 May 2016 / Published: 7 June 2016
(This article belongs to the Special Issue Lvov—Warsaw School)
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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. View Full-Text
Keywords: fuzzy set; fuzzy preference structure; fuzzy topology fuzzy set; fuzzy preference structure; fuzzy topology
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Kerre, E.E.; D´eer, L.; Van Gasse, B. An Overview of the Fuzzy Axiomatic Systems and Characterizations Proposed at Ghent University. Axioms 2016, 5, 17.

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