Several data from real world applications involves overlapping classes. Data is allowed to belong to multiple classes with different membership degrees. In this paper, we explore a different concept characterizing social networks, documents, and most of biological and chemical datasets: data could have multiple classes, but dominant classes are better noticed than dominated classes. For example, a document could discuss economy and politics, but it would be more focused on politics. A molecule could have multiple odors, but experts could notice some odors better than others. We are interested in this type of data, where a dominance relation exists between classes. Experts could easily make mistakes because dominated classes are hardly noticed. Data incoherence is a serious problem but not the only one. There is too much irrelevant and redundant attributes. Unfortunately this increases the computational time of generating classifiers. Our first challenge is to find an adapted model to overlapping classes considering dominance relations. The second challenge is to find the most relevant attributes. Finally the third challenge is to ensure that the approach gives results in an acceptable time. We address those challenges by taking advantage of the rough set theory, which is suited for incoherent data and allows multiple classes and attributes selection. The proposed approach works in a parallel and decentralized way to reduce the computational time. We tested it on real chemical data and the collected results are very promising.