Abstracting the signification from an amorphous conglomerate of data requires appropriate techniques for making patent some latent cognitive structures. This paper is devoted to the challenging case when fuzzy-termed data occur in a survey. The fuzzy paradigm is inherently assumed, but the representation formalism related to it induces a higher complexity in the semantic structure of the universe of discourse we have to deal with. In order to disclose the cognitive structures underlying fuzzy information systems, we are led to explore suitable metric concepts equipping the space of fuzzy-valued variables and the space of fuzzy-described individuals, respectively. This is crucial for laying the foundations of multivariate fuzzy-termed data analysis. Some natural algorithmic consequences following from the conceptual and formal generalizations mentioned above are explored in turn, namely the principal component analysis, the automatic classification and the methods of inducing graphical models, which are all extended to allow the processing of fuzzy-termed data.