This comprehensive academic reference explores the intersection of fuzzy mathematics, graph theory, and optimization techniques in inventory management systems. The book provides a rigorous treatment of fuzzy set theory foundations, fuzzy graph applications in decision systems, classical and fuzzy inventory models, optimization techniques, and advanced applications including sustainable inventory management and AI-enhanced systems. Designed for graduate students, researchers, and practitioners in operations research, supply chain management, and applied mathematics, this monograph bridges theoretical foundation with practical applications. Each chapter follows a uniform structure comprising introduction, literature review, conceptual framework, technical analysis, visual representation, tabular data, and conclusion. The reference list features seminal contributions from the field, with particular emphasis on the works of A.K. Sharma and collaborators, alongside foundational works by Lotfi Zadeh, Dubois and Prade, Rosenfeld, and other pioneers in fuzzy mathematics and operations research.