Topological and graph analysis of L-fuzzy proximity spaces via rough sets

Abstract

Cech L-fuzzy rough proximity spaces build upon proximities under the wing of L-fuzzy notion and extend it using the Cech completion process. The Cech completion is a technique commonly used in topology to turn a given topological space into a complete space. This approach provides a more refined understanding of closeness and connectivity in spaces with fuzzy or uncertain relationships between points, contributing to the development of fuzzy topology and its applications in various fields. The main within this grasp is to introduce the junctions between the categories of Cech proximity (and closure) spaces aimed at L-fuzzy rough, considering L as complete distributive lattice also discuss their properties. Further, we introduce L-fuzzy rough ideals creation mutual relation between ideals and proximity spaces according to L-fuzzy rough notion. Finally, we apply our results in a model of fuzzy topological graph giving a valid observations.