Interpretability in Fuzzy Systems Optimization: A Topological Approach

When dealing with complex problems, it is often the case that fuzzy systems must undergo an optimization process. During this process, the preservation of interpretability is a major concern. Here we present a new mathematical framework to analyze the notion of interpretability of a fuzzy partition, and a generic algorithm to preserve it. This approach is rather flexible and it helps to highly automatize the optimization process. Some tools come from the field of algebraic topology.