Fuzzy ordering relation and fuzzy poset

Authors:
Branimir Šešelja;Andreja Tepavčević
Affiliations:
Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia;Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia
Venue:
PReMI'07 Proceedings of the 2nd international conference on Pattern recognition and machine intelligence
Year:
2007

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Abstract

Connections between (weakly) reflexive, antisymmetric and transitive lattice-valued fuzzy relations on a nonempty set X (fuzzy ordering relations on X) and fuzzy subsets of a crisp poset on X (fuzzy posets) are established and various properties of cuts of such structures are proved. A representation of fuzzy sets by cuts corresponding to atoms in atomically generated lattices has also been given.