The SMAA-TODIM approach: Modeling of preferences and a robustness analysis framework

TODIM (an acronym in Portuguese of interactive and multicriteria decision making), which is founded on nonlinear cumulative prospect theory, has attracted increasing attention from the academic world since 1991. Up to now, a variety of TODIM multicriteria decision models have been developed and applied for solving decision making problems in a wide range of industries. In this study, we point out a limitation of TODIM, which is shared by all the TODIM-based models. Three types of inputs inherent in TODIM, i.e., criteria measurements, criteria weights and the attenuation factor of the losses, are usually uncertain. Moreover, these uncertainties may exist in TODIM at the same time, which has not been well investigated in the literature. To address this limitation, we apply stochastic multiobjective acceptability analysis (SMAA) to TODIM and therefore put forward the SMAA-TODIM method, to explore simultaneously the uncertainties inherent in the inputs of TODIM. In addition, a SMAA-TODIM-based robustness analysis framework for TODIM models is presented, based on which, the decision analyst can measure how robust a decision result is. Finally, applications of the robustness analysis framework for TODIM models are demonstrated by two examples.