Similarity Measures and Energy-Based Decision-Making in Intuitionistic Fuzzy Rough Graphs

Abstract A novel intuitionistic fuzzy rough similarity measure for classifying intuitionistic fuzzy rough graphs (IFRG) is presented in this study. Using both objective and subjective, it presents intuitionistic fuzzy rough preference relationships (IFRPRs) to assess the reputation ratings of experts. This approach improves decision-making by considering various competing criteria. To improve the decision-making process, the study also integrates energy concepts–energy $$\left(E\right)$$ , Laplacian energy $$\left(LE\right)$$ , and signless Laplacian energy $$\left(SLE\right)$$ –into IFRG. The study examines eigenvalue characteristics, emphasizing the boundaries of $$E$$ , $$LE$$ , and $$SLE$$ , and shows how suggested approaches might be used in real-time to choose renewable energy sources. The findings reveal that these approaches effectively address complex decision-making challenges. It incorporates sophisticated energy measures into IFRGs and provides a framework for assessing expert reputation ratings. The study uses two methods–the similarity measure and IFRG’s $$E$$ , $$LE$$ , and $$SLE$$ –to resolve decision-making concerns and evaluates several competing aspects to establish criteria relevance. It validates the efficacy of the suggested procedures through example. Graphical abstract