Dealing with imprecise inputs in a fuzzy rule-based system using an implication-based rule model

We discuss the means to efficiently propagate imprecise (but crisp) inputs in fuzzy control-like rule based systems in which fuzzy rules are chained in several levels. We consider a genuine implication-based model, in contrast to most of classical fuzzy control systems, using Rescher-Gaines implication to model the gradual relation between premises and conclusion of rules. The result of each inference is a crisp interval and we propose an efficient and sound method that provides with the tightest output intervals at one reasoning level, propagate them as input in the next level, and only pick a precise value at the very last level.