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This work demonstrates generalizing conditions for fuzzy connections in directed graphs and sets, suggesting broader applications.
This work extends our research on fuzzy relational Galois connections, previously established in the context of complete Heyting algebras, to the broader framework of arbitrary residuated lattices. In this context, we study the properties of fuzzy closure relations and fuzzy closure systems, and the relationship with fuzzy relational Galois connections. The main result of the paper is the generalization of the necessary and sufficient conditions for the existence of a right adjoint for a fuzzy relation linking a fuzzy transitive directed graph to an unstructured set.
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Cabrera et al. (2026) studied this question.
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