RT Journal Article
T1 Attribute implications with unknown information based on weak Heyting algebras
A1 Cordero-Ortega, Pablo
A1 Enciso-García-Oliveros, Manuel
A1 Mora, Angel
A1 Pérez-Gámez, Francisco
K1 Álgebra
AB Simplification logic, a logic for attribute implications, was originally defined for Boolean sets. It was extended to distributive fuzzy sets by using a complete dual Heyting algebra. In this paper, we weaken this restriction in the sense that we prove that it is possible to define a simplification logic on fuzzy sets in which the membership value structure is not necessarily distributive. For this purpose, we replace the structure of the complete dual Heyting algebra by the so-called weak complete dual Heyting algebra. We demonstrate the soundness and completeness of this simplification logic, and provide a characterisation of the operations defining weak complete dual Heyting algebras.
PB Elsevier
YR 2024
FD 2024-08
LK https://hdl.handle.net/10630/31758
UL https://hdl.handle.net/10630/31758
LA eng
NO Cordero, Pablo, Enciso, Manuel, Mora, Ángel, Pérez-Gámez, Francisco (2024), Attribute implications with unknown information based on weak Heyting algebras, Fuzzy Sets and Systems, Volume 490, 2024, 109026, ISSN 0165-0114
NO Funding for open access charge: Universidad de Málaga/CBUA
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026