Bi-monotonic fuzzy sets lead to optimal fuzzy interfaces

In this paper, we address the issue of designing optimal fuzzy interfaces, which are fundamental components of fuzzy models. In particular, we prove that for a class of so-called bi-monotonic fuzzy sets, optimal interfaces can be guaranteed if mild conditions hold. The class of bi-monotonic fuzzy sets covers a broad range of fuzzy sets shapes, including convex fuzzy sets, so that the provided theoretical results can be applied to a wide range of fuzzy models. As a practical result, the paper provides a set of guidelines that can be followed for the design of optimal fuzzy interfaces.