Analyzing user behavior on social networks to understand psychological traits is of growing importance. Structuring data extracted from users' concurrent activity across various platforms as a multiplex network can provide valuable insights. However, conventional approaches are limited by their reliance on explicit relationships, which are often private, and their use of single-source data. Therefore, this paper proposes a novel two-stage framework for personality type prediction. Its primary innovation is the use of an implicit relationship network, extracted from the fusion of multi-source, multi-modal data include text, image, and location, instead of relying on explicit friendship links. In the first stage, community structures in the multiplex network are identified using a multi-objective evolutionary approach (MOEA/D-TS), and then the implicit relationship network is constructed using a link prediction method (CLPES). In the second stage, the resulting network is leveraged as an information source within a machine learning framework to predict user personality types. Evaluations demonstrate the proposed framework's significant superiority. The final model, using a Random Forest classifier with the fusion of all three data sources, achieved an average Macro-F1 score of 0.673. This represents an average performance improvement of 23% compared to single-source models. This finding confirms the value of analyzing implicit relations and fusing multi-source data for a deeper understanding of user personality.