RT journal article
T1 Bipolar equations on complete distributive symmetric residuated lattices: The case of a join-irreducible right-hand side
A1 Cornejo Piñero, María Eugenia
A1 Lobo Palacios, David
A1 Medina Moreno, Jesús
A1 DeBaets, Bernard
A2 Matemáticas
K1 Bipolar equation
K1 Distributive symmetric residuated lattice
K1 Negation operator
K1 Irreducible element
AB Bipolar max-∗equations, with ∗a triangular norm, have recently become a popular research topic embedded in the broad field of fuzzy relational equations. In this paper, we lift the work from the restrictive setting of the real unit interval — obfuscating the underlying lattice-theoretical essence — to the general setting of complete distributive symmetric residuated lattices, allowing to build upon the vast body of knowledge on unipolar sup-∗equations on complete distributive residuated lattices. We determine the full solution set, with particular emphasis on the extremal solutions, of a bipolar sup-∗equation in case the right-hand side is a join-irreducible element. The results are illustrated by means of ample examples.
PB ELSEVIER
SN 0165-0114
YR 2022
FD 2022
LK http://hdl.handle.net/10498/26921
UL http://hdl.handle.net/10498/26921
LA eng
NO Partially supported by the 2014–2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in projects TIN2016-76653-P and PID2019-108991GB-I00, and with the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia in project FEDER-UCA18-108612, and by the European Cooperation in Science & Technology (COST) Action CA17124. BDB received funding from the Flemish Government under the “Onderzoeksprogramma Artificiële Intelligentie (AI) Vlaanderen” programme.
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026