Stochastic and epistemic uncertainty propagation in LCA

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). 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 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.3

Monte Carlo vs. Fuzzy Monte Carlo Simulation for Uncertainty and Global Sensitivity Analysis

“…A large difference in the distance implies that the predicted outputs are strongly influenced by unknown inputs that have an epistemic nature. In addition, the plausibility and belief distribution denote optimistic and pessimistic outcomes, respectively [5,6]. If the building stakeholders (e.g., architect, owner, engineer, and occupants) have optimistic preferences about the model risks, the plausibility distribution should be used for risk-based decision support.…”

“…However, it is difficult to clearly distinguish between an aleatory and epistemic uncertainty due to relative gaps of knowledge and the different physical or experimental capacities of each simulation user [5,6,9]. Nevertheless, Kiureghian [9] insisted that "distinction between aleatory and epistemic is useful for identifying sources of uncertainty that can be reduced, and in developing sound risk and reliability models".…”

“…Fuzzy set theory introduced by Zadeh [11] is an effective approach for representing epistemic uncertainty under imperfect knowledge. In the fuzzy set theory, fuzzy numbers are defined as convex and normalized fuzzy sets over the universal set with their fuzzy set membership functions that can be represented as a degree of likelihood between 0 and 1 [5,6,[12][13][14][15]. In general, the triangular fuzzy number (TFN) has been widely used ( Figure 1).…”

“…The fuzzy MCS combines a probability theory of MCS with a possibility theory of fuzzy arithmetic and can acquire a probabilistic output with a family of probability distributions, rather than a single probability distribution. The family of probability distributions can represent the model risks as a range between plausibility (lower limit) and belief (upper limit) [5,6]. The goal of this study is to compare the MCS to the fuzzy MCS with the aim of finding influential design options.…”

A pathway to circular economy: Developing a conceptual framework for complex value assessment of resources recovered from waste

“…RRfW systems are inherently dynamic and non-linear (Clavreul et al, 2013). New technologies and materials are developed, capital stocks degrade, customers' preferences change, and previously abundant resources become depleted.…”