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Multi-attribute decision-making (MADM) problems widely exist in real world. This paper investigates a type of MADM problems, in which the performances of the alternatives on attributes are represented in three different formats simultaneously, namely: 1) precise number; 2) probability density function; and 3) fuzzy linguistic judgment. Based on the imprecise weights on attributes, optimization models are constructed to determine the range of the distance between each alternative and the ideal solution (anti-ideal solution). Further, a ranking approach based on the TOPSIS method is proposed for the problem. This paper provides a new way to solve hybrid multi-attribute decision making problems with imprecise weights.