Incorporating uncertainty in the PROMETHEE MCDA method

Analyses of complex decision-making problems, involving tradeoffs among multiple criteria, is often undertaken using the PROMETHEE multi-criteria decision analysis (MCDA) outranking technique. Various sources of uncertainty exist in the application of MCDA methods including the definition of criteria weights and the assignment of criteria performance values. Generalized criterion functions were incorporated in PROMETHEE to take the uncertainty in the criteria performance values into account; however, actors find it extremely difficult to select the generalized criterion functions and their associated thresholds for each criterion, which therefore results in an additional source of uncertainty. Furthermore, the generalized criterion functions do not address the subjectivity and uncertainty in the criteria weights, therefore, this form of uncertainty is usually assessed by sensitivity analysis methods. In this paper, a reliability-based approach is proposed which enables the decision maker to examine the robustness of the solution obtained from PROMETHEE. The proposed approach therefore allows a decision to be made with confidence that the alternative chosen is the best performing alternative under the range of probable circumstances, without being required to define the generalized criterion functions. The proposed stochastic method involves defining the uncertainty in the input values using probability distributions, performing a reliability analysis by Monte Carlo simulation and undertaking a significance analysis using the Spearman rank correlation coefficient. The outcomes of the approach include a distribution of the total flows of each alternative based upon the expected range of input parameter values. The benefits of the approach are illustrated by applying it to a renewable energy case study.