Abstract
The extension of the fuzzy TOPSIS method based on the combination weight is presented to deal with multiple attribute decision-making problems under risk where the attribute value takes the form of the continuous random variable on the bounded intervals. First, the risk decision matrix is normalized by the transformation of the density function, and the variation coefficient method is used to determine the objective weights based on the expectations of the random variables. Subsequently, according to the maximizing rule of the weighted synthetic value of alternatives, the synthetic weight model is established. Then, the ideal solution and negative ideal solution is defined, the distances between the alternatives and the ideal/negative ideal solutions, and the relative closeness coefficients are calculated. In addition, the alternatives are ranked by the relative closeness coefficient of the alternatives. Finally, an illustrative example with the interval number is given to demonstrate the steps and the effectiveness of the proposed method.