Title: On the Second Accuracy of Generalized Approximation Spaces via Graph Neighborhood Structures
Authors: Y?usief S. Eassa
Volume: 10
Issue: 4
Pages: 8-12
Publication Date: 2026/04/28
Abstract:
This paper introduces a generalized approximation framework derived from graph structures using neighborhood and non-neighborhood relations of vertices. By associating each vertex with specific subsets of the vertex set, new graph-induced spaces are constructed which generate generalized approximation spaces. Based on these spaces, second lower and upper approximations are defined together with their boundary, positive, and negative regions. Several fundamental properties and theorems related to these approximations are established. Illustrative examples are presented to clarify the behavior of the proposed model.