Quasi-coincident neighborhood structure of relative I-fuzzy topology and its applications

In this paper, we consider the topic of the quasi-coincident neighborhood structure of relative I-fuzzy topology on a fuzzy subset in the sense of Guido. First we establish a kind of quasi-coincident relation on any fuzzy subset, and construct a kind of neighborhood system, called relative I-fuzzy quasi-coincident neighborhood system. Then, we find that relative I-fuzzy topology and relative I-fuzzy quasi-coincident neighborhood system can be obtained one from the other. Furthermore, as an application of relative I-fuzzy quasi-coincident neighborhood systems, the first countability, the second countability, and the separability degree of relative I-fuzzy topological space are investigated.