Decision-making algorithm based on the energy of interval-valued hesitant fuzzy soft sets

Interval-valued hesitant fuzzy soft sets, a powerful tool for data modeling, have been the focus of numerous studies. In addition to their various applications, examining the properties and characteristics of these structures from a theoretical mathematical perspective enables more efficient utilization in real-world problems. The primary objective of this research is to define a numerical characteristic of an interval-valued hesitant fuzzy soft set, analogous to the energy of a graph and the energy of a fuzzy soft set. The motivation for introducing this numerical characteristic lies in its potential to develop a decision-making algorithm that outperforms existing approaches addressing the same problem. The energy of a graph, as well as the energy of a fuzzy soft set, is defined as a norm function obtained by summing the singular values of the corresponding representation matrix. In optimization problems, this sum of singular values is known as the nuclear norm, which serves as the basis for introducing the notion of energy in interval-valued hesitant fuzzy soft sets. The results of the proposed algorithm are compared in this paper with those of various existing algorithms designed to solve the same problem. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025.