Grey stochastic multi-criteria decision-making based on regret theory and TOPSIS

Extended grey numbers (EGNs), integrated with discrete grey numbers and continuous grey numbers, have a powerful capacity to express uncertainty and thus have been widely studied and applied to solve multi-criteria decision-making (MCDM) problems that involve uncertainty. Considering stochastic MCDM problems with interval probabilities, we propose a grey stochastic MCDM approach based on regret theory and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), in which the criteria values are expressed as EGNs. We also construct the utility value function, regret value function, and perceived utility value function of EGNs, and we rank the alternatives in accordance with classical TOPSIS method. Finally, we provide two examples to illustrate the method and make comparison analyses between the proposed approach and existing methods. The comparisons suggest that the proposed approach is feasible and usable, and it provides a new method to solve stochastic MCDM problems. It not only fully considers decision-makers’ bounded rationality for decision-making, but also enriches and expands the application of regret theory.