期刊
IEEE TRANSACTIONS ON FUZZY SYSTEMS
卷 30, 期 11, 页码 4788-4799出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2022.3160326
关键词
Fuzzy sets; Kernel; Shortest path problem; Writing; Upper bound; Uncertainty; Topology; Admissible orders; fuzzy numbers; fuzzy weighted graphs; orders on fuzzy numbers
资金
- CNPq (Brazilian Research Council) [311429/2020-3]
- Spanish Government [PID2019-108392GB-I00]
This article introduces the concept of admissible order for fuzzy numbers and proposes a method to construct admissible orders. With this method, the path costs in fuzzy weighted graphs can be ranked.
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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