Stochastic multicriteria decision-making approach based on SMAA-ELECTRE with extended gray numbers

Actual stochastic multicriteria decision-making (MCDM) problems usually exhibit two forms of information loss: criteria value uncertainty and criteria weight uncertainty. In this paper, extended gray numbers (EGNs), integrated with discrete gray numbers and interval gray numbers are used to express the uncertainty of stochastic MCDM problems. Stochastic multicriteria acceptability analysis (SMAA) and ELECTRE III are combined to solve stochastic MCDM problems with uncertain weight information. First, the outranking relations on interval gray numbers and EGNs are defined. Then, a SMAA-ELECTRE model for dealing with gray stochastic MCDM problems is constructed. Finally, an illustrative example and two comparative analyses are provided to verify the feasibility and usability of the proposed approach. The proposed approach provides recommendations for alternatives based on uncertain preference information. It therefore contributes a new way to solve stochastic MCDM problems with uncertain, imprecise, and/or missing preference information.