Admissible Orders on Fuzzy Numbers
Bedregal, Benjamin
Universidade Federal do Rio Grande do Norte
Bustince, Humberto
Universidad Publica de Navarra
Diaz, Roberto
Universidad de Los Lagos
Journal
IEEE Transactions on Fuzzy Systems
ISSN
1063-6706
1941-0034
Open Access
green
Volume
30
Start page
4788
End page
4799
From the more than two hundred partial orders for fuzzy numbers proposed in the literature, only a few are total. In this article, we introduce the notion of admissible order for fuzzy numbers equipped with a partial order, i.e., a total order which refines the partial order. In particular, it is given special attention to the partial order proposed by Klir and Yuan in 1995. Moreover, we propose a method to construct admissible orders on fuzzy numbers in terms of linear orders defined for intervals considering a strictly increasing upper dense sequence, proving that this order is admissible for a given partial order. Finally, we use admissible orders to ranking the path costs in fuzzy weighted graphs.
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