Abstract: A grey correlation rank method is presented to solve the problems of multiple attribute decision-making(MADM) under risk with weight unknown and attribute value as continuous random variable on bounded intervals.To begin with,the risk decision matrix is normalized by density function,a deviation between two random variables is defined by expectation value,and the maximizing deviation rule is used to determine the weights of attributes.Then,positive/negative ideal solutions are defined.The grey correlation degrees between alternatives and positive/negative ideal solutions and the relative closeness coefficients are calculated.Furthermore,the alternatives are ranked by the relative closeness coefficients of alternatives.Finally,an MADM example with interval number is given to demonstrate the steps and effectiveness of the proposed method.