dc.contributor.author | Gutiérrez García, Francisco Javier | |
dc.contributor.author | Höhle, Ulrich | |
dc.contributor.author | Kubiak, Tomasz | |
dc.date.accessioned | 2024-02-08T08:39:11Z | |
dc.date.available | 2024-02-08T08:39:11Z | |
dc.date.issued | 2018-07-10 | |
dc.identifier.citation | Fuzzy Sets and Systems 370 : 63-78 (2019) | |
dc.identifier.issn | 0165-0114 | |
dc.identifier.issn | 1872-6801 | |
dc.identifier.uri | http://hdl.handle.net/10810/64920 | |
dc.description.abstract | The original Hutton interval I (L) can algebraically be identified with the tensor product I ⊗ L of the real unit interval I and a complete lattice L. Due to this, the tensor product M ⊗ L with M a completely distributive lattice is considered as a generalization of the lattice I (L). When appropriately endowed with an L-topology, the tensor product M ⊗ L becomes also an L-topological extension of I (L). If M is ▹-separable (= it has a countable join base free of supercompact elements), many of the L-topological features of I (L) are retained. To wit, Urysohn lemma and Tietze–Urysohn extension theorem for (M ⊗ L)-valued functions are then proved. The relationship of M ⊗ L to the L-fuzzy topological modification of M in the sense of D. Zhang and Y.-M. Liu [27] is discussed. | es_ES |
dc.description.sponsorship | The authors gratefully acknowledge support from the Ministry of Economy and Competitiveness of Spain (grant MTM2015-63608-P (MINECO/FEDER)
Basque Government (grant IT974-16) | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | Elsevier | es_ES |
dc.relation | info:eu-repo/grantAgreement/MINECO/MTM2015-63608-P | |
dc.rights | info:eu-repo/semantics/openAccess | es_ES |
dc.subject | Hutton fuzzy unit interval | es_ES |
dc.subject | the category sup | |
dc.subject | tensor product of complete lattices | |
dc.subject | completely distributive lattice | |
dc.subject | supercompact | |
dc.subject | ▹-separability | |
dc.subject | Urysohn lemma | |
dc.subject | Tietze–Urysohn extension theorem | |
dc.subject | L-fuzzy modification of complete distributivity | |
dc.subject | symmetric monoidal closed category | |
dc.title | An extension of the fuzzy unit interval to a tensor product with completely distributive first factor | es_ES |
dc.type | info:eu-repo/semantics/preprint | es_ES |
dc.rights.holder | © 2018 Elsevier | |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S0165011418303695 | |
dc.identifier.doi | 10.1016/j.fss.2018.07.002 | |
dc.departamentoes | Matemáticas | es_ES |
dc.departamentoeu | Matematika | es_ES |