Fuzzy Graph-Based Financial Network Analysis for Risk Assessment, Portfolio Optimization, and Decision Support

Amruta Nagesh Chitari

Abstract

Financial networks are complex systems characterized by interconnected relation-ships among various entities such as banks, insurers, and investment firms. These relationships often involve uncertainty, ambiguity, and incomplete information, which traditional graph models struggle to capture effectively. Fuzzy graph theory offers a powerful alternative by incorporating degrees of uncertainty through fuzzy sets and membership functions. This paper explores the application of fuzzy graphs in finan-cial networks, focusing on risk assessment and management. It discusses how fuzzy graphs can model credit risk propagation, systemic risk analysis, and fraud detection in an uncertain environment. The integration of fuzzy logic enables more realistic and flexible representations of financial interdependencies, enhancing the ability to iden-tify vulnerabilities and assess the robustness of financial systems. Through theoretical frameworks and practical case studies, the paper highlights the advantages and chal-lenges of using fuzzy graphs, offering insights into how they can support more informed decision-making in complex financial ecosystems.

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