Decision-Making and Clustering Algorithms Based on the Scored-Energy of Hesitant Fuzzy Soft Sets

This paper introduces a novel numerical characteristic of hesitant fuzzy soft sets called their scored-energy. We introduce this concept as a combination of two very different tools, namely, scores of hesitant fuzzy elements and singular values of a (not- necessarily square) matrix. The latter idea replicates the concept of energy or nuclear norm of a matrix, which has excellent analytical abilities in graph theory and applications in fields such as statistics or signal processing. Natural algorithms establish applications of scored-energies to both clustering and decision-making. Through examples, we demonstrate how these new techniques are efficient and implementable in practice. Comparisons are conducted that prove their validity, reliability, and credibility.