Algorithms for Decision-Making Based on Energies of Probabilistic and Dual Probabilistic Soft Set

Abstract

After introducing the concepts of soft sets and graph energy as independent terms from different areas of mathematics, there has been significant application of both concepts. The theory of soft sets has been combined with other theories, such as fuzzy set theory and probability theory. From this combination with probability theory, a structure known as probabilistic soft set has emerged, which has been discussed relatively little in the context of decision-making. In this paper, we propose new decision-making algorithms based on numerical characteristics, which we call energies of probabilistic soft sets and dual probabilistic soft sets. The introduced concept of energy for probabilistic soft sets and dual probabilistic soft sets originated from integrating the idea of graph energy into probabilistic soft sets. The paper also presents a comparison of the obtained results using energy with results obtained by other algorithms.