A neutrosophic open set–based multi-criteria decision framework for sustainable lithium-ion battery waste management under uncertainty

This chapter introduces a novel neutrosophic open set–based multi-criteria decision-making (MCDM) framework for evaluating sustainable lithium-ion battery (LIB) waste management strategies under uncertainty. Motivated by the increasing environmental challenges associated with end-of-life battery disposal in electric vehicles and renewable energy systems, the proposed methodology integrates single-valued neutrosophic sets (SVNSs) and neutrosophic topology to represent uncertainty, inconsistency, and incomplete expert knowledge through independent truth, indeterminacy, and falsity membership functions. Unlike conventional fuzzy and intuitionistic fuzzy approaches, the framework employs neutrosophic open sets as flexible sustainability regions, allowing decision alternatives to exhibit graded memberships across overlapping environmental and regulatory criteria. A mathematically bounded criterion-weighted neutrosophic aggregation function is developed to evaluate alternatives, and its theoretical robustness is established through formal proofs of boundedness, monotonicity, convexity, consistency under trivial uncertainty, and topological consistency. To validate feasibility and practical applicability, the model is applied to a comparative sustainability assessment of mechanical and chemical recycling, landfill disposal, and pyrometallurgical recovery for lithium-ion battery waste management under multiple criteria, including economic feasibility, environmental safety, technological maturity, and regulatory compliance. A comprehensive sensitivity analysis under varying decision-maker preference weights confirms ranking stability and robustness across scenarios, consistently identifying recycling-based strategies as the most sustainable option. The proposed framework advances neutrosophic decision science by introducing a structural topological layer into MCDM and provides a resilient, interpretable, and mathematically rigorous decision-support mechanism for environmental sustainability, circular economy planning, waste governance, and technology evaluation under uncertainty.