The theory of three-way decisions is to consider a decision-making problem as a ternary classification one which is realized by the acceptance, rejection and non-commitment. Recently, this theory has been integrated with formal concept analysis in two different ways: constructive and axiomatic methods. The constructive method is to define certain three-way concepts in a formal context to support three-way concept analysis, while the axiomatic one is to characterize general three-way concepts by axioms so as to perform three-way concept learning. Nevertheless, there are similarities between the constructive and the axiomatic methods. In fact, both three-way concept analysis induced by the constructive method and three-way concept learning induced by the axiomatic one are realized by incorporating the idea of ternary classification into the design of extent or intent of a concept. However, their information fusion abilities need to be improved since neither of them is able to deal with large or multi-source data effectively. Motivated by this problem, our paper is to reconsider three-way concept learning based on cognitive operators from the perspective of information fusion. That is, the parallel computing techniques of learning three-way concepts are developed for large and multi-source data. Specifically, for large data, the relationship between the global granular concept and the local ones is first clarified, and then it is employed to design an information fusion algorithm. For multi-source data, the whole evaluation function used to induce three-way decisions is established by aggregating the results obtained in each single-source data, and three-way concept learning is made by constructing lower and upper approximation concepts. Finally, we conduct some numerical experiments to evaluate the effectiveness of the proposed parallel computing algorithms. (C) 2017 Elsevier Inc. All rights reserved.