Analysis of computer communication networks based on evaluation of domination and double domination for interval-valued T-spherical fuzzy graphs and their applications in decision-making problems

This research introduces the Interval-Valued T-Spherical Fuzzy Graph (IVTSFG), a novel extension of fuzzy graph theory designed to address imprecision in decision-making processes, network analysis, and Computer Communication Networks (CCNs). Integrating four types of membership degrees-membership, non-membership, abstinence, and hesitancy-the IVTSFG framework significantly enhances the ability to model and analyze complex systems with uncertain data. The study explores the theories of domination and double domination within the context of IVTSFGs, presenting new methods for evaluating network resilience and optimization. Key findings include the development of innovative techniques for applying domination and double domination in IVTSFGs, demonstrating improved performance in managing CCNs. Comparative analysis with existing fuzzy graph models highlights the advantages of IVTSFGs, particularly in capturing nuanced relationships within network structures. The research provides practical examples and empirical comparisons, showcasing the framework's effectiveness in various decision-making scenarios.