Categories of L-Fuzzy Internal (Enclosed) Relations

A. A. Ramadan ()
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A. A. Ramadan: Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 02, 457-486

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

Keywords: Complete residuated lattice; L-fuzzy internal (enclosed) relation; L-fuzzy interior (closure) operators; L-fuzzy quasi-proximity (uniformity) spaces; Galois correspondence (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500206

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