Cognitive social structures (CSS) is an area in social network research that has enduring importance but lacks flexible models. In this paper we consider statistical models for CSS systems where we observe a three-dimensional binary array of relational ties characterized by the “sender” of the relation, the “receiver” of the relation, and the “perceiver” of the relation from the “sender” to the “receiver”. Such systems have been represented as networks by Krackhardt. Durante, Dunson and Vogelstein proposed a flexible Bayesian nonparametric approach to model the population distribution of network valued data, in which the joint distribution of the edges probabilities is defined through a mixture model that reduces dimensionality and incorporates information within each mixture component based on latent space models. Inspired by this work, we modify the model to characterize cognitive social structures by adding a parameter for cognitive error. As a case study, we apply our model to Krackhardt's network data of 21 managers in a high-tech machine manufacturing firm. The results show distinct effects of cognitive error and illustrate that our model is capable of characterizing cognitive social structures. The results also motivate future improvement on transitivity and triangle relations.