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Fuzzy Rule-Based Classification Systems are a widely used tool in Data Mining because of the interpretability given by the concept of linguistic label. However, the use of this type of models implies a degree of uncertainty in the definition of the fuzzy partitions. In this work we will use the concept of Interval-Valued Fuzzy Set to deal with this problem. The aim of this contribution is to show the improvement in the performance of linguistic Fuzzy Rule-Based Classification Systems afterward the application of a cooperative tuning methodology between the tuning of the amplitude of the support and the lateral tuning (based on the 2-tuples fuzzy linguistic model) applied to the linguistic labels modeled with Interval-Valued Fuzzy Sets.