Admissible Orders on Fuzzy Numbers - Zumelzu Carcamo, Nicolas Eduardo; Bedregal, Benjamin; Mansilla Villarroel, Jose Edmundo; Bustince, Humberto; Diaz, Roberto (My University, 2022)
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.
Keywords: fuzzy sets; kernel; shortest path problem; writing; upper bound; uncertainty; topology; admissible orders; fuzzy numbers; fuzzy weighted graphs; orders on fuzzy numbers