To address the issues of counter-intuitive phenomena and data value limitations in existing intuitionistic fuzzy multiple attribute decision-making methods, this paper proposes an intuitionistic fuzzy sum weighted exponential information (SWEI) multiple attribute decision-making method based on the Lemoine point. Firstly, inspired by the geometric concept of the triangular Lemoine point, a new intuitionistic fuzzy similarity measure is designed and its axiomatic properties are rigorously proven. Comparative analysis with existing intuitionistic fuzzy similarity measures demonstrates that this measure not only characterizes the similarity between intuitionistic fuzzy numbers more reasonably, but also effectively overcomes the drawbacks of missing axiomatic properties and computational infeasibility. Then, based on this similarity measure, a score function is constructed to reduce computational complexity in the decision-making process. Next, an intuitionistic fuzzy score matrix is established using the score function, and the weights of alternative are determined via the entropy weight method. The weighted exponential information is then utilized to rank and select the optimal alternative. Finally, the effectiveness of the proposed method is validated through case study and simulation analyses. Sensitivity analysis and comparative experiments further demonstrate the stability and superiority of the proposed method.