Admissible orders on fuzzy numbers

Nicolás Zumelzu; Benjamin Bedregal; Edmundo Mansilla; Humberto Bustince; Roberto Díaz

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arXiv · 2003.01530

Admissible orders on fuzzy numbers

Nicolás Zumelzu·Benjamin Bedregal·Edmundo Mansilla·Humberto Bustince·Roberto Díaz

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Abstract

From the more than two hundred partial orders for fuzzy numbers proposed in the literature, only a few are total. In this paper, 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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BibTeX RIS

Nicolás Zumelzu, Benjamin Bedregal, Edmundo Mansilla, Humberto Bustince, Roberto Díaz. 2020-03-01. Admissible orders on fuzzy numbers. https://arxiv.org/abs/2003.01530

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