Currently, we are witnessing a growing trend in the study and application of problems in the framework of
Big Data. This is mainly due to the great advantages which come from the knowledge extraction from a
high volume of information. For this reason, we observe a migration of the standard Data Mining systems
towards a new functional paradigm that allows at working with Big Data. By means of the MapReduce
model and its different extensions, scalability can be successfully addressed, while maintaining a good
fault tolerance during the execution of the algorithms. Among the different approaches used in Data Mining,
those models based on fuzzy systems stand out for many applications. Among their advantages, we
must stress the use of a representation close to the natural language. Additionally, they use an inference
model that allows a good adaptation to different scenarios, especially those with a given degree of uncertainty.
Despite the success of this type of systems, their migration to the Big Data environment in the
different learning areas is at a preliminary stage yet. In this paper, we will carry out an overview of the
main existing proposals on the topic, analyzing the design of these models. Additionally, we will discuss
those problems related to the data distribution and parallelization of the current algorithms, and also its
relationship with the fuzzy representation of the information. Finally, we will provide our view on the
expectations for the future in this framework according to the design of those methods based on fuzzy
sets, as well as the open challenges on the topic
