Applying Fuzzy and Probabilistic Uncertainty Concepts to the Material Flow Analysis of Palladium in Austria

Material flow analysis (MFA) is a widely applied tool to investigate resource and recycling systems of metals and minerals. Owing to data limitations and restricted system understanding, MFA results are inherently uncertain. To demonstrate the systematic implementation of uncertainty analysis in MFA, two mathematical concepts for the quantification of uncertainties were applied to Austrian palladium (Pd) resource flows and evaluated: (1) uncertainty ranges expressed by fuzzy sets and (2) uncertainty ranges defined by normal distributions given as mean values and standard deviations. Whereas normal distributions represent the traditional approach for quantifying uncertainties in MFA, fuzzy sets may offer additional benefits in relation to uncertainty quantification in cases of scarce information. With respect to the Pd case study, the fuzzy representation of uncertain quantities is more consistent with the actual data availability in cases of incomplete databases, and fuzzy sets serve to highlight the effect of uncertainty on resource efficiency indicators derived from the MFA results. For both approaches, data reconciliation procedures offer the potential to reduce uncertainty and evaluate the plausibility of the model results. With respect to Pd resource management, improved formal collection of end-of-life (EOL) consumer products is identified as a key factor in increasing the recycling efficiency. In particular, the partial export of EOL vehicles represents a substantial loss of Pd from the Austrian resource system, whereas approximately 70% of the Pd in the EOL consumer products is recovered in waste management. In conclusion, systematic uncertainty analysis is an integral part of MFA required to provide robust decision support in resource management.