We focus on various kinds of generalizations of (ordinary) fuzzy sets. In our opinion, the most important ones are: intuitionistic fuzzy sets, interval-valued fuzzy sets and type-2 fuzzy sets. We discuss each of them, and put emphasis on motivation for such a generalization. So the main aim is not to bring new results, the paper only summarizes known facts concerning generalizations of fuzzy sets. Moreover, the intersection, union, complement and inclusion for ordinary / intuitionistic / interval-valued / type-2 fuzzy sets are compared.