Hybrid random multi-criteria decision-making approach with incomplete certain information

For a hybrid multi-criteria decision-making problem with incomplete certain information, in which criteriapsilas values are deterministic numbers, interval numbers, linguistic terms, triangle fuzzy numbers and random variables, a new approach based on TOPSIS is proposed. In this approach, we transform the random variables and the linguistic terms into interval numbers and triangle fuzzy numbers respectively at first. Then, the normalized decision matrix is constructed, from which the ideal and negative ideal solutions are attained. A nonlinear programming model is established to get the criteria weights, and the alternatives are ranked by the closeness degree to the ideal and negative ideal solutions at last. At the end of the paper, a numerical example is given to show the feasibility and availability of the method.