Aiming at hybrid multiple attribute decision-making under the risk of interval probability with weight unknown, a
decision approach based on entropy weight and projection theory is presented. Firstly, the transformation from the linguistic
variables and uncertain linguistic variables to the trapezoidal fuzzy numbers is established, and the mixed decision data
is changed into a single trapezoidal fuzzy number. Then, the risk decision matrix is transformed into certain decision
matrix by expectation value, and entropy weight method is used to determine the weights of attributes. On the basis of
the attribute weights, the weighted decision matrix is calculated and the alternatives are ranked by relative closeness degree
of the projection value from each alternative to the ideal solution and to negative ideal solution. Finally, an application case
is given to demonstrate effectiveness of the proposed approach.