Some Concepts of Interval Valued Pythagorean Fuzzy Graphs and Analysis of Socioeconomic Conditions of Communities

The concepts of covering and matching in fuzzy graphs have played a significant role in addressing problems within uncertain and imprecise environments. Numerous real-world problems in decision-making, network optimization etc have been investigated through these concepts in the domains of fuzzy graphs, intuitionistic fuzzy graphs etc. However, the concepts of covering and matching have not yet been explored within the framework of interval-valued Pythagorean fuzzy graphs (IVPyFGs). To fill this gap, we extend these notions within IVPyFGs and utilize them to analyze socioeconomic conditions across different communities. Initially, we introduce several key terms related to covering such as strong arcs (SAs), strong node cover (SNC) and strong node covering number (SNCN), and characterized different kinds of IVPyFGs including complete-IVPyFGs and complete bipartite IVPyFGs based on these terms. Following this, we introduce the concepts of matching in IVPyFGs and explore several characterizations several specific types of IVPyFGs. To demonstrate the effectiveness of this study, we apply these newly established concepts to analyze the socioeconomic conditions of various communities. Finally, a comparative study is conducted to verify that our proposed model is more efficient than existing models.