<p>The aim of this study is to address the multi-criteria group decision-making problems, where decision information is expressed by experts using single-valued or interval-valued fuzzy linguistic terms, with both expert weights and criteria weights being unknown. This paper proposes a novel method that combines the merits of distance entropy and the interval rough number cloud model, for handling uncertain information. Firstly, criteria weights are determined using distance entropy applied to interval rough numbers, which are derived from a fuzzy linguistic decision matrix containing single-valued or interval-valued. Secondly, expert weights are determined by measuring deviations between each expert’s individual decision matrix and those of other experts. Thirdly, construct an interval rough number cloud model based decision matrix to aggregate decision information via the determined expert weights and criteria weights. Finally, alternatives are ranked based on cloud closeness degrees, which are calculated via the TOPSIS method. To validate the method’s effectiveness, this paper presents a case study on failure mode and effects analysis, for the single-point mooring system of a floating production storage and offloading vessel in the South China Sea. The proposed method yields the following advantages: (1) it enhances decision-making accuracy in complex and uncertain environments; (2) it minimizes information loss; (3) it effectively handles both the inherent uncertainty of decision data and the randomness of the decision-making process.</p>