@misc{10498/26921,
year = {2022},
url = {http://hdl.handle.net/10498/26921},
abstract = {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.},
organization = {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.},
publisher = {ELSEVIER},
keywords = {Bipolar equation},
keywords = {Distributive symmetric residuated lattice},
keywords = {Negation operator},
keywords = {Irreducible element},
title = {Bipolar equations on complete distributive symmetric residuated lattices: The case of a join-irreducible right-hand side},
doi = {10.1016/j.fss.2022.02.003},
author = {Cornejo Piñero, María Eugenia and Lobo Palacios, David and Medina Moreno, Jesús and DeBaets, Bernard},
}