Semantic interpretability in hierarchical fuzzy systems: Creating semantically decouplable hierarchies

Analysing the interpretability of a fuzzy system (either hierarchical or not) involves consideration of its semantic properties and evaluation of its structural complexity. The present paper concentrates on the semantic aspects of interpretability in hierarchical fuzzy systems. Complexity reduction is also considered, but from the perspective of its interaction with semantic preservation. In that sense, the paper shows that only the use of intermediate variables with meaning (interpretable variables) will transform the complexity reduction into a real improvement in interpretability. The paper formalises this idea by introducing the concept of semantically decouplable hierarchies. Under the assumption of semantic decouplability, it is shown that the interpretability of the overall hierarchical system can be directly obtained from that of its subsystems. Consequently, the paper defines and measures the interpretability of a semantically decouplable hierarchical fuzzy system as the aggregation of the interpretability of its subsystems. Finally, several options will be considered for this aggregation process.