Stochastic and epistemic uncertainty propagation in LCA

  • Julie ClavreulEmail author
  • Dominique Guyonnet
  • Davide Tonini
  • Thomas H. Christensen



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.


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.


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.


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



The case study presented in this paper was based on the work by Hamelin et al. (2012) and Tonini et al. (2012). We are grateful to Lorie Hamelin for making some background data available.

Supplementary material

11367_2013_572_MOESM1_ESM.pdf (321 kb)
ESM 1 (PDF 320 kb)


  1. André JCS, Lopes DR (2012) On the use of possibility theory in uncertainty analysis of life cycle inventory. Int J Life Cycle Assess 17:350–361CrossRefGoogle Scholar
  2. Ardente F, Beccali M, Cellura M (2004) F.A.L.C.A.D.E.: a fuzzy software for the energy and environmental balances of products. Ecol Model 176:359–379CrossRefGoogle Scholar
  3. Baudrit C, Guyonnet D, Dubois D (2005) Post-processing the hybrid approach for addressing uncertainty in risk assessments. Environ Eng 131:1750–1754CrossRefGoogle Scholar
  4. Baudrit C, Dubois D, Guyonnet D (2006) Joint propagation and exploitation of probabilistic and possibilistic information in risk assessment models. IEEE Trans Fuzzy Syst 14:593–608CrossRefGoogle Scholar
  5. Benetto E, Dujet C, Rousseaux P (2008) Integrating fuzzy multicriteria analysis and uncertainty evaluation in life cycle assessment. Environ Model Softw 23:1461–1467CrossRefGoogle Scholar
  6. Chevalier J-L, Le Téno JF (1996) Life cycle analysis with ill-defined data and its application to building products. Int J Life Cycle Assess 1:90–96CrossRefGoogle Scholar
  7. Clavreul J, Guyonnet D, Christensen TH (2012) Quantifying uncertainty in LCA-modelling of waste management systems. Waste Manage 32:2482–2495CrossRefGoogle Scholar
  8. Couso I, Moral S, Walley P (2000) A survey of concepts of independence for imprecise probabilities. Risk Decis Policy 5:165–181CrossRefGoogle Scholar
  9. Cruze N, Goel PK, Bakshi BR (2013) On the “rigorous proof of fuzzy error propagation with matrix-based LCI”. Int J Life Cycle Assess 18:516–519CrossRefGoogle Scholar
  10. Dalgaard R, Schmidt JH, Halberg N, Christensen P, Thrane M, Pengue WA (2008) LCA of soybean meal. Int J Life Cycle Assess 13:240–254CrossRefGoogle Scholar
  11. Danish Energy Agency, (2010) Technology Data for Energy Plants. Danish Energy Agency, Copenhagen, Denmark. . Accessed 4 December 2012
  12. DONG Energy A/S,, Vattenfall A/S (2010) Livscyklusvurdering - Dansk el og kraftvarme (In Danish). Accessed 3 December 2012
  13. Dubois D (2006) Possibility theory and statistical reasoning. Comput Stat Data Anal 51:47–69CrossRefGoogle Scholar
  14. Dubois D, Prade H (1988) Possibility theory. Plenum, New YorkCrossRefGoogle Scholar
  15. Dubois D, Prade H (2008) Possibility theory: an approach to computerized processing of uncertainty. Plenum, New YorkGoogle Scholar
  16. Dubois D, Prade H (2009) Formal representations of uncertainty. In: Bouyssou D, Dubois D, Pirlot M, Prade H (eds) Decision-making process-concepts and methods. Chapter 3. London: ISTE & Wiley, pp 85–156Google Scholar
  17. Dubois D, Guyonnet D (2011) Risk-informed decision-making in the presence of epistemic uncertainty. Int J Gen Syst 40:145–167CrossRefGoogle Scholar
  18. Edwards R, Mulligan D, Marelli L (2010) Indirect land use change from increased biofuels demand. Comparison of models and results for marginal biofuels production from different feedstocks. Luxembourg: Publications Office of the European Union. Accessed 27 September 2012
  19. Energistyrelsen (2011) Forudsætninger for samfundsøkonomiske analyser på energiområdet (In Danish). Danish Energy Agency, Copenhagen, Denmark. Accessed 27 September 2012
  20. Ferson S, Ginzburg LR (1996) Different methods are needed to propagate ignorance and variability. Reliability Eng Syst Saf 54:133–144CrossRefGoogle Scholar
  21. Frischknecht R, Jungbluth N, Althaus HJ, Doka G, Dones R, Heck T, Hellweg S, Hischier R, Nemecek T, Rebitzer G, Spielmann M (2005) The ecoinvent database: overview and methodological framework. Int J Life Cycle Assess 10:3–9CrossRefGoogle Scholar
  22. Gonzàlez B, Adenso-Dìaz B, Gonzàlez-Torre PL (2002) A fuzzy logic approach for the impact assessment in LCA. Resour Conserv Recycl 37:61–79CrossRefGoogle Scholar
  23. Guereca LP, Agell N, Gasso S, Baldasano JM (2007) Fuzzy approach to life cycle impact assessment—an application for biowaste management systems. Int J Life Cycle Assess 12:488–496Google Scholar
  24. Guyonnet D, Bourgine B, Dubois D, Fargier H, Côme B, Chilès JP (2003) Hybrid approach for addressing uncertainty in risk assessments. Environ Eng 129:68–78CrossRefGoogle Scholar
  25. Hamelin L, Jorgensen U, Petersen BM, Olesen JE, Wenzel H (2012) Modelling the carbon and nitrogen balances of direct land use changes from energy crops in Denmark: a consequential life cycle inventory. Glob Change Biol Bioenergy 4:889–907CrossRefGoogle Scholar
  26. Heijungs R, Tan RR (2010) Rigorous proof of fuzzy error propagation with matrix-based LCI. Int J Life Cycle Assess 15:1014–1019CrossRefGoogle Scholar
  27. Hong J, Shaked S, Rosenbaum RK, Jolliet O (2010) Analytical uncertainty propagation in life cycle inventory and impact assessment: application to an automobile front panel. Int J Life Cycle Assess 15:499–510CrossRefGoogle Scholar
  28. Huijbregts MAJ, Gilijamse W, Ragas AMJ, Reijnders L (2003) Evaluating uncertainty in environmental life-cycle assessment. A case study comparing two insulation options for a Dutch one-family dwelling. Environ Sci Technol 37:2600–2608CrossRefGoogle Scholar
  29. Hurwicz L (1951) Optimality criteria for decision making under ignorance. Cowles Commission discussion paper, Statistics No. 370Google Scholar
  30. Imbeault-Tétreault H, Jolliet O, Deschênes L, Rosenbaum RK (2013) Analytical propagation of uncertainty in life cycle assessment using matrix formulation. J Ind Ecol. doi: 10.1111/jiec.12001 Google Scholar
  31. Lindley DV (1971) Making decisions. Wiley-Interscience, LondonGoogle Scholar
  32. Lloyd SM, Ries R (2007) Characterising, propagating and analyzing uncertainty in life-cycle assessment, a survey of quantitative approaches. J Ind Ecol 11:161–179CrossRefGoogle Scholar
  33. Morgan MG, Henrion M (1990) Uncertainty: a guide to dealing with uncertainty in quantitative risk and policy analysis. Cambridge University Press, New YorkCrossRefGoogle Scholar
  34. Reap J, Roman F, Duncan S, Bras B (2008) A survey of unresolved problems in life cycle assessment, Part 1: goal and scope and inventory analysis. Int J Life Cycle Assess 13:290–300CrossRefGoogle Scholar
  35. Schmidt JH (2008) System delimitation in agricultural consequential LCA—outline of methodology and illustrative case study of wheat in Denmark. Int J Life Cycle Assess 13:350–364CrossRefGoogle Scholar
  36. Searchinger TD (2010) Biofuels and the need for additional carbon. Environ Res Lett 5:024007CrossRefGoogle Scholar
  37. Searchinger TD, Heimlich R, Houghton RA, Dong F, Elobeid A, Fabiosa J, Tokgoz S, Hayes D, Yu TH (2008) Use of U.S. croplands for biofuels increases greenhouse gases through emissions from land-use change. Science 319:1238–1240CrossRefGoogle Scholar
  38. Shafer G (1976) A mathematical theory of evidence. Princeton University PressGoogle Scholar
  39. Shulman N, Feder M (2004) The uniform distribution as a universal prior. IEEE Trans Inform Theory 50:1356–1362CrossRefGoogle Scholar
  40. Sonnemann GW, Schuhmacher M, Castells F (2003) Uncertainty assessment by a Monte Carlo simulation in a life cycle inventory of electricity produced by a waste incinerator. J Cleaner Prod 11:279–292CrossRefGoogle Scholar
  41. Tan R (2008) Using fuzzy numbers to propagate uncertainty in matrix-based LCI. Int J Life Cycle Assess 13:585–592CrossRefGoogle Scholar
  42. Tan R, Culaba AB, Purvis MRI (2004) POLCAGE 1.0—a possibilistic life-cycle assessment model for evaluating alternative transportation fuels. Environ Model Softw 19:907–918CrossRefGoogle Scholar
  43. Thabrew L, Lloyd S, Cypcar CC, Hamilton JD, Ries R (2008) Life cycle assessment of water-based acrylic floor finish maintenance programs. Int J Life Cycle Assess 13:65–74Google Scholar
  44. Tonini D, Astrup T (2012) Life-cycle assessment of biomass-based energy systems: a case study for Denmark. Appl Energy 99:234–246CrossRefGoogle Scholar
  45. Tonini D, Hamelin L, Wenzel H, Astrup T (2012) Bioenergy production from perennial energy crops: a consequential LCA of 12 bioenergy scenarios including land use changes. Environ Sci Technol 46(24):13521–13530CrossRefGoogle Scholar
  46. Weckenmann A, Schwan A (2001) Environmental life cycle assessment with support of fuzzy-sets. Int J Life Cycle Assess 6:13–18CrossRefGoogle Scholar
  47. Weidema B (2003) Market information in life cycle assessment. Environmental Project No. 863 2003 Miljøprojekt. Danish Environmental Protection Agency. Accessed 27 September 2012
  48. Weidema B, Frees N, Nielsen AM (1999) Marginal production technologies for life cycle inventories. Int J Life Cycle Assess 4:48–56CrossRefGoogle Scholar
  49. Williams E, Weber C, Hawkins T (2009) Hybrid approach to managing uncertainty in life cycle inventories. J Ind Ecol 15:928–944CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Julie Clavreul
    • 1
    Email author
  • Dominique Guyonnet
    • 2
  • Davide Tonini
    • 1
  • Thomas H. Christensen
    • 1
  1. 1.Technical University of Denmark, Department of Environmental EngineeringKongens LyngbyDenmark
  2. 2.BRGM, ENAG (BRGM School)Orléans cedexFrance

Personalised recommendations