Abstract
This paper reveals some relationships between [Formula: see text]-fuzzy internal (enclosed) relations and [Formula: see text]-fuzzy interior (closure) spaces in a categorical framework. Also, we prove that there exist many interesting Galois connections between the category of all discrete [Formula: see text]-fuzzy interior (closure) spaces and the category [Formula: see text]-fuzzy internal (enclosed) relations. Moreover, the category [Formula: see text]-fuzzy of internal relations, the category of [Formula: see text]-fuzzy quasi-uniform spaces and the category of [Formula: see text]-fuzzy quasi-proximity spaces are investigated.
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