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A novel evolutionary TSK-subsethood fuzzy-neural network model along with its parallel implementation on a LAM/MPI cluster is presented in this paper. The proposed four-layered network is inspired by the subsethood class of models, which have ability to seamlessly compose numeric and linguistic data simultaneously. The proposed model embeds TSK rules into the network architecture, while transmitting information using subsethood products and a linear weighted sum of fuzzy sets. L-R arithmetic is used in the internal operation of the network. Differential evolution learning is employed to evolve tunable parameters of the network. A parallel implementation using a master-slave approach efficiently distributes the computational load of string evaluations on a LAM/MPI cluster.The proposed model is tested on two benchmark problems: Iris Classification, Mackey Glass time series prediction.