Abstract
Closure is a key concept in several branches of mathematics. This work presents a definition of fuzzy closure relation and relational closure system on fuzzy transitive digraphs. The core of the paper is the study of the properties of these structures. As expected, fuzzy closure relations and relational closure systems are related, but the relationship among them is not one-to-one. Last section of the paper shows the search for some characterizations for that one-to-one relation to hold.
Supported by the State Agency of Research (AEI), the Spanish Ministry of Science, Innovation, and Universities (MCIU), the European Social Fund (FEDER), the Junta de Andalucía (JA), and the Universidad de Málaga (UMA) through the FPU19/01467 (MCIU) internship and the research projects with reference PGC2018-095869-B-I00, TIN2017-89023-P (MCIU/AEI/FEDER, UE) and UMA2018-FEDERJA-001 (JA/UMA/FEDER, UE).
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Ojeda-Hernández, M., Cabrera, I.P., Cordero, P., Muñoz-Velasco, E. (2022). Relational Extension of Closure Structures. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_7
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