Neutrosophic Probability and Measure for Resilient Supply Chain Management under Indeterminacy

Abstract

Supply chains face two kinds of uncertainty: random variation and indeterminacy caused by missing, delayed, or conflicting information. This paper models both by using a neutrosophic representation that attaches to every key quantity a triplet for support, indeterminacy, and refutation. Building on this, we define neutrosophic measure and probability for supply-chain events, and we embed them in linear and mixed-integer programs that remain feasible under worst-case demand. The framework provides clear operators for aggregating evidence, converting triplets to actionable intervals, and ranking alternatives with a risk-averse score. We evaluate the approach in three studies. First, supplier selection with an explicit reliability share shifts volume toward trustworthy sources while meeting capacity and reducing total cost. Second, demand forecasting translates ambiguous signals into effective intervals that, when added to a simple baseline, lower mean absolute percentage error and maintain full coverage of realized demand. Third, transportation planning uses a tunable share on a high-availability path to trade cost for improved plan availability. Across all cases, enforcing robust balance removes indeterminacy from service, while neutrosophic metrics quantify where uncertainty remains and what it costs. The method is transparent, easy to audit, and compatible with standard optimization tools, making it practical for resilient planning.