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Organizers |
On the fuzzy ordered sets
by
Abdelaziz Amroune
Laboratory of Pure and Applied Mathematics, M'sila University, P.O.Box 166 Ichbilia, M'sila 28105, ALGERIA.
Coauthors: Lemnaouar ZEDAM
There are two type of relations which often arise in mathematics: order relations and equivalence relations. An order relation is a generalization of both set inclusion and the order relation on real line. The theory of fuzzy relations was initiated by Zadeh [10]. In that seminal paper he introduced the concept of a fuzzy relation on a nonempty set X as a fuzzy subset of X×X, defined the notion of similarity as a generalization of the notion of equivalence, and defined the concept of fuzzy order by generalizing the notions of reflexivity, antisymmetry and transitivity. Since then many notions and results from the theory of ordered sets have been extend to the fuzzy ordered sets. Some of these results can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9].
The aim of this note is to present some basic properties of fuzzy order and prove some known results of ordered sets including Dedekind-MacNeille completion theorem for fuzzy ordered sets.
References
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Zadeh L. A., Similarity relations and fuzzy orderings, Info. Sci., 3(1971), 177-200.
Date received: April 30, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caug-23.