Fractional Calculus for Neutrosophic-Valued Functions and Its Application in an Inventory Lot-Sizing Problem

Past experiences and memory significantly contribute to self-learning and improved decision-making. These can assist decision-makers in refining their strategies for better outcomes. Fractional calculus is a tool that captures a system’s memory or past experience through its repeating patterns. In the realm of uncertainty, neutrosophic set theory demonstrates greater suitability, as it independently assesses membership, non-membership, and indeterminacy. In this article, we aim to extend the theory further by introducing fractional calculus for neutrosophic-valued functions. The proposed method is applied to an economic lot-sizing problem. Numerical simulations of the lot-sizing model suggest that strong memory employment with a memory index of 0.1 can lead to an increase in average profit in memory-independent phenomena with a memory index of 1 by approximately 44% to 49%. Additionally, the neutrosophic environment yields superior profitability results compared to both precise and imprecise settings. The synergy of fractional-order dynamics and neutrosophic uncertainty modeling paves the way for enhanced decision-making in complex, ambiguous environments.