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Characterising Quasi-Closed Elements via Closure Systems on Complete Fuzzy Lattices
Pub. online: 22 April 2026      Type: Research Article      Open accessOpen Access
Received
1 July 2025
Accepted
1 April 2026
Published
22 April 2026

Abstract

The notion of quasi-closed element plays a central role in several branches of mathematics and computer sciences, for instance, in the Duquenne-Guigues basis of attribute implications. This paper deals with the extension of quasi-closed elements to the fuzzy setting by extending the well-known characterisation of quasi-closed elements in the crisp case, which is given in terms of closure systems. Specifically, we provide two distinct definitions, one considering crisp closure systems and another for fuzzy ones. Finally, we obtain a characterisation for each one of these notions.

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Biographies

Ojeda-Hernández Manuel
manuojeda@uma.es

M. Ojeda-Hernández is an assistant professor at the Department of Algebra, Geometry and Topology of the Universidad de Málaga. His research is devoted to mathematics under uncertainty, fuzzy algebraic structures, formal concept analysis and their applications.

Cabrera Inma P.
ipcabrera@uma.es

IP. Cabrera PhD mathematics, MSc mathematics, is an associate professor at the Applied Mathematics Department of the Universidad de Málaga. She is specialized in the mathematical foundations of information processing techniques and data science, specifically in the presence of uncertainty, imprecise or vague information. Her areas of expertise include fuzzy logic, fuzzy formal concept analysis and non-deterministic structures.

Cordero Pablo
pcordero@uma.es

P. Cordero is a full professor at the Applied Mathematics Department of the Universidad de Málaga. He is specialized in fuzzy mathematics, lattice theory, formal concept analysis, logic and automated reasoning methods.

Muñoz-Velasco Emilio
ejmunoz@uma.es

E. Muñoz-Velasco PhD mathematics, MSc mathematics, is an associate professor at the Applied Mathematics Department of the Universidad de Málaga. He is specialized in non-classical logic, fuzzy set theory, fuzzy formal concept analysis and non-deterministic structures.


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Copyright
© 2026 Vilnius University
Open access article under the CC BY license.

Keywords
closure operator complete lattice fuzzy logic quasi-closed

Funding
This work has been partially funded by the State Agency of Research (AEI), the Ministerio de Ciencia, Innovación y Universidades (MCIU), the European Social Research Fund (FEDER), the Junta de Andalucía (JA), y la Universidad de Málaga (UMA) through the PhD grant FPU19/01467 (MCIU), the VALID research project (PID2022-140630NB-I00 funded by MCIN/AEI/10.13039/501100011033) and the research project PID2021-127870OB-I00 (MCIU/AEI/FEDER, UE).

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