(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we introduced the concept of the heptapartitioned neutrosophic soft set (HP-NSS), a novel extension and generalization of the neutrosophic soft set theory. To improve accuracy, the indeterminacy is divided into five additional possibilities, which are as follows: absolute true, relative true, contradiction, unknown, and ignorance, relative false and absolute false. We extend the concept of neutrosophic soft topological spaces by introducing heptapartitioned neutrosophic soft topological spaces (HPNSTS), a novel generalization that incorporates seven distinct partitions to model uncertainty, vagueness, and indeterminacy in topological structures. Three new definitions are introduced and these definitions are p-open, pre-open and semi-open sets. Special attention is focused on p-open sets, and a number of results related to p-open sets are addressed. Machine learning and graphical algorithms, such as K-Means clustering, Heat maps, Elbow method, Feature correlation, 2D-normalized t-SNE, and parallel coordinates of 3D T-SNE, were used and visualized for a real-world application involving the romantic feelings of young boys and girls across various dimensions.