Energy based bipolar intuitionistic fuzzy digraph decision-making system in selecting COVID-19 vaccines

Abstract

The energy of a graph, defined as the absolute sum of the eigenvalues (EIGs) of its adjacency matrix, has been applied to numerous research fields, including decision-making techniques. It can be defined for a fuzzy graph when the graph has uncertain vertices and edges. A bipolar intuitionistic fuzzy graph (BIFG) is an extended version of fuzzy graph that helps to deal with uncertainty in an effective manner. Therefore, this study unites the above-said concepts to examine the energy concepts with additional information and utilizes them in the decision-making problem to explore their applicability. Initially, the notions, relations and bounds of the energy, Laplacian energy (LE) and signless Laplacian energy (SLE) are defined. Further, a novel energy-based multi-criteria decision-making (MCDM) technique is designed by utilizing the energy of BIFG to obtain the objective weights for the decision experts. The selection problem of five COVID-19 vaccines with respect to eight important criteria is taken to elucidate the proposed decision-making technique, where Moderna has resulted as the finest vaccine among other vaccines. Moreover, a comparative is done with the correlation and distance measures to show the superiority of the proposed method. Finally, a sensitivity analysis is done to depict the reliability of the proposed technique.