# Stochastic and epistemic uncertainty propagation in LCA

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## Abstract

### Purpose

When performing uncertainty propagation, most LCA practitioners choose to represent uncertainties by single probability distributions and to propagate them using stochastic methods. However, the selection of single probability distributions appears often arbitrary when faced with scarce information or expert judgement (epistemic uncertainty). The possibility theory has been developed over the last decades to address this problem. The objective of this study is to present a methodology that combines probability and possibility theories to represent stochastic and epistemic uncertainties in a consistent manner and apply it to LCA. A case study is used to show the uncertainty propagation performed with the proposed method and compare it to propagation performed using probability and possibility theories alone.

### Methods

Basic knowledge on the probability theory is first recalled, followed by a detailed description of epistemic uncertainty representation using fuzzy intervals. The propagation methods used are the Monte Carlo analysis for probability distribution and an optimisation on alpha-cuts for fuzzy intervals. The proposed method (noted as Independent Random Set, IRS) generalizes the process of random sampling to probability distributions as well as fuzzy intervals, thus making the simultaneous use of both representations possible.

### Results and discussion

The results highlight the fundamental difference between the probabilistic and possibilistic representations: while the Monte Carlo analysis generates a single probability distribution, the IRS method yields a family of probability distributions bounded by an upper and a lower distribution. The distance between these two bounds is the consequence of the incomplete character of information pertaining to certain parameters. In a real situation, an excessive distance between these two bounds might motivate the decision-maker to increase the information base regarding certain critical parameters, in order to reduce the uncertainty. Such a decision could not ensue from a purely probabilistic calculation based on subjective (postulated) distributions (despite lack of information), because there is no way of distinguishing, in the variability of the calculated result, what comes from true randomness and what comes from incomplete information.

### Conclusions

The method presented offers the advantage of putting the focus on the information rather than deciding a priori of how to represent it. If the information is rich, then a purely statistical representation mode is adequate, but if the information is scarce, then it may be better conveyed by possibility distributions.

## Keywords

Confidence index Distribution Fuzzy sets Intervals Possibility Probability Uncertainty propagation Uncertainty representation## Notes

## Supplementary material

## References

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