Abstract
Galois connection in category theory palys an important role in establish the relationships between different spatial structures. In this paper, we prove that there exist many interesting Galois connections between the category of Alexandroff $L$-fuzzy topological spaces and the category of reflexive $L$-fuzzy relations.
Highlights
Hajek [8] introduced a complete residuated lattice which is an algebraic structure for many valued logic
We prove that there exist many interesting Galois connections between the category of Alexandroff L-fuzzy topological spaces and the category of reflexive L-fuzzy relations
Kim [13, 14] investigated the properties of various approximation operators and Alexandroff topologies in complete residuated lattices
Summary
Hajek [8] introduced a complete residuated lattice which is an algebraic structure for many valued logic. Fang and Yue [7] studied the relationship between L-fuzzy closure systems and L-fuzzy topological spaces from a category viewpoint for a complete residuated lattice L. Studied the relationship between L-fuzzy interior systems and L-fuzzy topological spaces over complete residuated lattices. Radzikowska [26, 27] developed fuzzy rough sets in complete residuated lattice. Ma and Hu [20] investigated the topological and lattice structures of L-fuzzy rough sets determined by lower and upper sets. Kim [13, 14] investigated the properties of various approximation operators and Alexandroff topologies in complete residuated lattices. We investigate the relationships between the category of Alexandroff L-fuzzy topological spaces and the category of reflexive L-fuzzy approximation spaces. We obtain some interesting adjunctions between the considered categories
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