Heptapartitioned Neutrosophic Soft Topologies and Machine Learning Techniques for Exploring Romantic Feelings (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.
Keywords: NSS, Heptapartitioned neutrosophic SS, Distance Measures, K-Means algorithm, Machine Learning Techniques, SVHNS Applications