In this paper, learning of the FCMs represented using triangular fuzzy numbers (TFNs) in their weight matrices is studied. For this aim a population based novel learning approach is proposed. In the proposed algorithm, BB-BC optimization method is preferred because of its fast convergence capability. Moreover, this proposed approach involves concept by concept (CbC) learning to increase the accuracy of the learning of FCMs. Two different tests are realized as case studies for investigating the performance of the learning approach. For the first test, the learning capability of the algorithm is examined and for the second test the performance of generalization capability is investigated. The tests, which are presented via tables and figures, show that learning approach is successful for learning of FCMs with TFNs. Furthermore, from the case study it can be seen that the uncertain information can be represented and interpreted by the proposed FCM design methodology in a more efficient way.