Convergence structures in ( L , M )-DFTML
Ahmed Aref Abd El-Latif · Journal of Intelligent & Fuzzy Systems · 2017
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 .