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The big data term is used to describe the exponential data growth that has recently occurred and represents an immense challenge for traditional learning techniques. To deal with big data classification problems we propose the Chi-FRBCS-BigData algorithm, a linguistic fuzzy rule-based classification system that uses the MapReduce framework to learn and fuse rule bases. It has been developed in two versions with different fusion processes. An experimental study is carried out and the results obtained show that the proposal is able to handle these problems providing competitive results.