RT journal article
T1 General and left-continuous operators on lattice-based sums
A1 García Aragón, Roberto
A1 Jara, Pascual
A1 Medina Moreno, Jesús
A2 Matemáticas
K1 T-norm
K1 Ordinal sum
K1 Horizontal sum
K1 Lattice sum
AB Lattice-based sum provides a procedure to obtain posets and lattices from families of posets and lattices, respectively. Establishing sufficient conditions to ensure the lattice structure was the most significant challenge achieved in previous works. Next steps are to consider structures with general operators defined on the lattices of the family, introduce a sum of these operators on the obtained lattice-based sum and study the properties preserved by this new definition. We will prove that the natural definition preserve, in general, the monotonicity, associativity, commutativity, etc. This paper also introduces a new mechanism focused on preserving the left-continuity property of the operators defined on the lattices. This new approach also preserves the associativity and the infimum of non-empty subsets, and takes into account (infinite) complete lattices, unlike the previous works.
PB Elsevier
SN 0165-0114
YR 2026
FD 2026
LK http://hdl.handle.net/10498/39079
UL http://hdl.handle.net/10498/39079
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 09-may-2026