In the present study, we propose a novel trapezium cloud-based TOPSIS (technique for order preference by similarity to ideal solution) method with interval-valued intuitionistic hesitant fuzzy linguistic (IVIHFL) information. We also propose a method to transform IVIHFL numbers into trapezium clouds. Novel weighted Hamming, Euclidean, and Hausdorff distance measures for trapezium clouds are also defined in the present study. Advantage of proposed TOPSIS method is that it includes characteristic of cloud model of handling both randomness and fuzziness of qualitative perceptions with linguistic information. To understand the methodology of proposed trapezium cloud-based TOPSIS with IVIHFL information, we include an example of decision-making in stock selection. Proposed method is also compared with an existing recent method. We also include a validity test to confirm the outperformance of the ranking to validate its out performance. The proposed trapezium cloud-based TOPSIS method incorporates uncertainty, hesitancy, and inconsistency using both qualitative and quantitative information; this makes the proposed method unique from other TOPSIS methods.