Decision-making algorithm based on the energy of interval-valued fuzzy soft sets
Ljubica Djurović, Maja Laković, Nenad Stojanović
TL;DR
The paper addresses decision-making under uncertainty by extending interval-valued fuzzy sets with soft-set structure (IVFSS) and introducing an energy-based numerical characteristic. It defines the pessimistic energy $E_{min}$ as the sum of singular values of the minimum-values matrix, the optimistic energy $E_{max}$ as the sum of singular values of the maximum-values matrix, and the overall energy $E^* = (E_{min} + E_{max})/2$. A decision-making algorithm based on these energies is proposed and validated on apartment and scenic-spot problems, showing improved handling of outliers and yielding a consistent ranking compared to several existing methods. The authors derive upper bounds $E_{min}, E_{max}, E^* \le n \sqrt{m}$ and discuss limitations and future directions, including weighting schemes and broader IVFSS applications.
Abstract
In our work, we continue to explore the properties of interval-valued fuzzy soft sets, which are obtained by combining interval-valued fuzzy sets and soft sets. We introduce the concept of energy of an interval-valued fuzzy soft set, as well as pessimistic and optimistic energy, enabling us to construct an effective decision-making algorithm. Through examples, the paper demonstrates how the introduced algorithm is successfully applied to problems involving uncertainty. Additionally, we compare the introduced method with other methods dealing with similar or related issues.