Modeling uncertainty in course selection using singular value decomposition-based energy measures within neutrosophic frameworks

Accurate course selection is an important step in a student’s academic and professional journey. Choosing the right course not only aligns with a student’s interests and strengths but also significantly influences their future career prospects. Making a well-informed decision based on a student’s background, interests, financial situation, and future requirements may involve uncertainty and vagueness due to incomplete information and data variability. To address such challenges, this paper advances neutrosophic soft set theory by introducing the energy measures of complex neutrosophic soft set using singular value decomposition, drawing upon concepts from graph energy and matrix representation. Earlier models such as graph energy, Pythagorean fuzzy graph energy, and neutrosophic set energy have contributed to uncertainty modeling but fall short when dealing with periodic or oscillatory data, where phase information is essential. The proposed complex neutrosophic soft set model addresses this limitation by incorporating complex-valued memberships, non-membership, and neutral degree. In addition, this paper proposes an algorithmic approach based on the energy measure of Complex Neutrosophic Soft Set to support well-informed decision-making. This approach is then applied to a case study involving the selection of a suitable course for a student from among three options: Software Engineering, Data Science, and Digital Marketing. The proposed algorithm yielded energy values of $$-$$ 1.196, 1.784, and $$-$$ 1.392 for Software Engineering, Data Science, and Digital Marketing, respectively. After normalization, Data Science achieved a preference score of 100%, making it the most suitable choice among the considered alternatives. Additionally, to ensure the effectiveness and validity of the proposed method, a comprehensive comparison is conducted with other energy-based models and multi-attribute decision-making techniques. Finally, the paper concludes with a summary of the research findings and outlines potential directions for future work.