International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1958 2020 2020 School of Advanced Sciences, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India Ankit Dubey School of Advanced Sciences, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India Ranjan Kumar This paper provides a comprehensive evaluation and categorization of the various uncertain environment employed by researchers and scientists to model and analyze inventory management systems in diverse sectors, including healthcare, supply chain, and routing issues. Additionally, it examines the challenges associated with the classical inventory model and introduces the concepts of fuzzy theory and the extended fuzzy principle in inventory management. The article presents important definitions related to fuzzy theory, including the fuzzy inventory model and its challenges. It also explores the applications of the extended fuzzy principle in real-life problems. The study focuses on inventory management under the extended fuzzy principle (Intuitionistic, Neutrosophic, Pythagorean, and so on), considering uncertain demand and imprecise data. The research contributes to the field by providing insights into the potential of fuzzy theory in overcoming the challenges of classical models and improving decision-making in inventory management. 2023 2023 08 20 10.54216/IJNS.210401 https://www.americaspg.com/articleinfo/21/show/1958