Convolution lattices
Fecha
2018Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
ES/1PE/TIN2016-77356-P
Impacto
|
10.1016/j.fss.2017.04.017
Resumen
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 ...
[++]
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. [--]
Materias
Algebra,
Convolution operations,
Lattice
Editor
Elsevier
Publicado en
Fuzzy Sets and Systems 335 (2018) 67–93
Departamento
Universidad Pública de Navarra. Departamento de Automática y Computación /
Nafarroako Unibertsitate Publikoa. Automatika eta Konputazioa Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute of Smart Cities - ISC
Versión del editor
Entidades Financiadoras
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.