The problem of mismatches between the categories ( some members may belong to more than one category)

The definitional problem (it is difficult or impossible to identify a set of necessary and sufficient conditions to define a category.

The problem of conceptual fuzziness (not all the categories have clear boundaries)

The problem of typicality (many categories exhibit typicality effects).

The problem of prototypicality ( some categories are formed around prototypes, while others - around salient examples)