Zumelzu, NicolásCallejas Bedregal, BenjaminMansilla, EdmundoBustince Sola, HumbertoDíaz, Roberto2022-08-302023-03-172022Zumelzu, N.; Bedregal, B.; Mansilla, E.; Bustince, H.; Diaz, R.. (2022). Admissible orders on fuzzy numbers. IEEE Transactions on Fuzzy Systems1063-670610.1109/TFUZZ.2022.3160326https://academica-e.unavarra.es/handle/2454/43887From 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. IEEEapplication/pdfeng© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other work.Admissible ordersFuzzy numbersFuzzy setsFuzzy weighted graphsKernelOrders on fuzzy numbersShortest path problemTopologyUncertaintyUpper boundWritingArtículo / Artikulua2022-08-30Acceso abierto / Sarbide irekiainfo:eu-repo/semantics/openAccess