Interpretability constraints for fuzzy information granulation

Information granules are complex entities that arise in the process of abstraction of data and derivation of knowledge. The automatic generation of information granules from data is an important task, since it gives to machines the ability of acquiring knowledge that can be communicated to users. For this purpose, knowledge acquisition should provide for fuzzy information granules that can be naturally labelled by linguistic terms, i.e. symbols that belong to the natural language. Information granules of this type are called interpretable. However, interpretability cannot be guaranteed until a set of constraints is imposed on the granulation process. In literature, several interpretability constraints have been proposed, but, due to the subjective interpretation of interpretability, there is no agreement on which constraints should be adopted. This survey is an attempt to provide for a complete presentation of interpretability constraints adopted in literature with the following objectives: (i) to give a homogeneous description of all interpretability constraints; (ii) to provide for a critical review of such constraints; (iii) to identify potentially different meanings of interpretability. Hopefully, this survey may serve as a guidance for designing interpretable fuzzy models as well as for identifying new methods of interpretable information granulation.