A novel multicriteria decision-making approach based on Pythagorean fuzzy sets and graph theory

Given the problem that the relations among alternatives or criteria cannot be handled well in multicriteria decision making, this paper applies the concept of Pythagorean fuzzy sets to the graph and develops a decision-making approach based on Pythagorean fuzzy graphs (PFGs). First, the weights obtained from the Laplacian energy of PFGs are taken as the subjective weights of criteria. Then, a new Pythagorean fuzzy entropy measure is defined to compute the objective weights of criteria. Meanwhile, a combined weighting method is presented, which makes the criteria weights consist of subjective weights and objective weights. Furthermore, combined weights are applied to the decision-making process and a graph-based Pythagorean fuzzy decision-making method is proposed. Compared with other existing techniques, the proposed approach considers the relations between alternatives and the relations between criteria simultaneously. Finally, an illustrative example is used to verify the approach and demonstrate its effectiveness. The results show that the alternative ranking obtained by the proposed approach is reliable and credible.