Affiliations: [a] Department of Mathematics, Faculty of Science and Arts at Belqarn, Sabt Al-Alaya, Bisha University, Saudi Arabia | [b]
High Institute of Computer King Marriott, Alexandria, Egypt
Correspondence:
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Corresponding author. A.A. Abd El-latif. E-mail: [email protected].
Abstract: Abd El-latif and Kim in [2], introduced the concepts of (L, M)-double fuzzy ideal and (L, M)-double fuzzy remote neighborhood systems, this paper is devoted to use these concepts to introduce and study the concept of pretopological fuzzy DR-convergence structure, and constructs the category PrFDRCS which contains TFDRCS as a bireflective subcategory. TFDRCS is shown as an isomorphic with (L, M)-TDFRN. Considering the relationship between the categories (L, M)-TDFRN and (L, M)-DFTML, it is proved that TFDRCS is isomorphic with (L, M)-DFTML. Also, pretopological fuzzy DR-convergence spaces have been found to be characterized as a kind of (L, M)-double fuzzy remote neighborhood spaces, which is called an (L, M)- strong double fuzzy remote neighborhood space. Finally, it was proved that the category (L, M)-SDFRN is isomorphic with the category PrFDRCS.
