Currently, big data and its applications have become one of the emergent topics. In practice, MapReduce framework and its different extensions are the most popular approaches for big data. Fuzzy system based models stand out for many applications. However, when a given observation has no overlap with antecedent values, no rule can be invoked in classical fuzzy inference can also appear in big data environment, and therefore no consequence can be derived. Fortunately, fuzzy rule interpolation techniques can support inference in such cases. Combining traditional fuzzy reasoning technique and fuzzy interpolation method may promote the accuracy of inference conclusion. Therefore, in this article, an initial investigation into the framework of MapReduce with dynamic fuzzy inference/interpolation for big data applications (BigData-DFRI) is reported. The results of an experimental investigation of this method are represented, demonstrating the potential and efficacy of the proposed approach.