Convolution lattices
| dc.contributor.author | Miguel Turullols, Laura de | |
| dc.contributor.author | Bustince Sola, Humberto | |
| dc.contributor.author | Baets, Bernard de | |
| dc.contributor.department | Automatika eta Konputazioa | eu |
| dc.contributor.department | Institute of Smart Cities - ISC | en |
| dc.contributor.department | Automática y Computación | es_ES |
| dc.date.accessioned | 2018-07-16T12:42:49Z | |
| dc.date.available | 2019-05-02T23:00:10Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract | We propose two convolution operations on the set of functions between two bounded lattices and investigate the algebraic structure they constitute, in particular the lattice laws they satisfy. Each of these laws requires the restriction to a specific subset of functions, such as normal, idempotent or convex functions. Combining all individual results, we identify the maximal subsets of functions resulting in a bounded lattice, and show this result to be equivalent to the distributivity of the lattice acting as domain of the functions. Furthermore, these lattices turn out to be distributive as well. Additionally, we show that for the larger subset of idempotent functions, although not satisfying the absorption laws, the convolution operations satisfy the Birkhoff equation. | en |
| dc.description.sponsorship | This work has been supported by the Research Services of the Universidad Publica de Navarra, and by the research project TIN2016-77356-P from MINECO, AEI/FEDER, UE. | en |
| dc.embargo.lift | 2019-05-02 | |
| dc.embargo.terms | 2019-05-02 | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1016/j.fss.2017.04.017 | |
| dc.identifier.issn | 0165-0114 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/29128 | |
| dc.language.iso | eng | en |
| dc.publisher | Elsevier | en |
| dc.relation.ispartof | Fuzzy Sets and Systems 335 (2018) 67–93 | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-P/ | |
| dc.relation.publisherversion | http://dx.doi.org/10.1016/j.fss.2017.04.017 | |
| dc.rights | © 2017 Elsevier B.V. The manuscript version is made available under the CC BY-NC-ND 4.0 license. | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Algebra | en |
| dc.subject | Convolution operations | en |
| dc.subject | Lattice | en |
| dc.title | Convolution lattices | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | |
| dspace.entity.type | Publication | |
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| relation.isAuthorOfPublication.latestForDiscovery | b6673ff1-b94d-4852-be93-90b30a9c8555 |