A PROMETHEE II Method Based on Regret Theory Under the Probabilistic Linguistic Environment

The PROMETHEE II method is useful for the decision-making problems to order the alternatives. This paper proposes a PROMETHEE II method based on regret theory under the probabilistic linguistic environment. The probabilistic linguistic evaluations are obtained by applying the basic unit-interval monotonic function-based method. At first, the obtained probabilistic linguistic evaluations are normalized and further transformed to the benefit types. Then, considering the psychological behavior of the decision-makers, the preference value of an alternative over others under each criterion is calculated by combining the regret theory. Hereafter, a group of preference values of an alternative over others under all criteria are weighted aggregated to the preference index. Afterwards, the preference indexes of an alternative over others and that of others over this alternative are aggregated to the outgoing flow and incoming flow respectively. Furthermore, the net-flow is obtained by operating the outgoing flow minus the incoming flow. The alternatives are ordered according to their net-flows. A problem for selecting the cloud serving for a college is resolved to verify the feasibility and the effectiveness of the proposed method.