Applications of Binary Intuitionistic Fine Topological Spaces for Digital Plane

In order to model computer images, digital spaces such as \(Z^{2}\) are utilized and the link between the classical topological spaces such as \(T_{1}, T_{1/2}, T_{0}\) spaces etc., and the digital spaces are studied by many authors to solve important connectivity problems, studying graphics, pattern recognition etc. In graph theoretical approach to solve connectivity contradictions 4 and 8 adjacencies serves as the basic. It is well known that key approaches to solve such problems are graph theoretic approach and topological approach. Traditional 4 and 8 adjacencies in a topology are considered in this article which aims to structure 4 and 8 adjacencies in a topology called binary intuitionistic fine topology \((\BI_fT)\). Initially 4 and 8 adjacencies-\(\BI_fT\) are constructed and operators such as 4 and 8-\(BI_fT\) interiors and closures are defined and their properties are discussed. Eventually, 4 and 8 connected-\(\BI_f\)-connected and non-connected points are defined and explained using example.