Mapping Love: A Heptapartitioned Neutrosophic Machine Learning Study of University Students’ Romantic Sensations (European Journal of Pure and Applied Mathematics, 2025)
This paper introduces the novel concept of single valued heptapartitioned neutrosophic sets (SVHNSs) which is the generalized version of the neutrosophic sets. This set consists of seven membership functions which are more sensitive to real-world problems. Membership functions are defined as an absolute true, relative true, absolute false, relative false, contradiction, unknown (undefined) and ignorance respectively. This scenario of indeterminacy provides a better accuracy.  Moreover, several properties of this set are also addressed. This study focuses on the romantic sensations experienced by young boys and girls in a variety of contexts. The dataset supporting this study comprises individuals aged 18–25, with data collected from the Psychology Department at Peshawar University, Pakistan. This data was critically analyzed using the Single-Valued Heptapartitioned Neutrosophic Set (SVHNS). For a real-world application involving the romantic feelings of young individuals across various dimensions, machine learning and graphical algorithms—such as Encrypted K-Means Clustering, Encrypted K-Means Clustering Heat Map, Encrypted Elbow Method, Decrypted K-Means Clustering, Encrypted Correlation Matrix, and Decrypted Correlation Matrix—were applied and visualized. These algorithms assist in examining and developing relationships among various factors that influence the romantic feelings of young men and women. The proposed techniques offer new dimensions not only for psychological studies in general but also specifically for understanding emotional disorders and breakups in romantic relationships among university students.
Keywords: Neutrosophic set; Single Valued Heptapartitioned Neutrosophic Set (SVHNS); Distance Measures; K-Means algorithm; Machine Learning Techniques; Applications of SVHNS