Santana, FagnerCallejas Bedregal, BenjaminViana, PetrucioBustince Sola, Humberto2020-07-022022-02-2620200165-011410.1016/j.fss.2020.02.009https://academica-e.unavarra.es/handle/2454/37281In this paper, we make some considerations about admissible orders on the set of closed subintervals of the unit interval I[0,1], i.e. linear orders that refine the product order on intervals. We propose a new way to generate admissible orders on I[0,1] which is more general than those we find in the current literature. Also, we deal with the possibility of an admissible order on I[0,1] to be isomorphic to the usual order on [0,1]. We prove that some orders constructed by our method are not isomorphic to the usual one and we make some considerations about the following question: is there some admissible order on I[0,1] isomorphic to the usual order on [0,1]?20 p.application/pdfeng© 2020 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0.Interval-valued fuzzy setsOrder isomorphismAdmissible orderCantor’s bijectioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess