Practical Inference With Systems of Gradual Implicative Rules

A general approach to practical inference with gradual implicative rules and fuzzy inputs is presented. Gradual rules represent constraints restricting outputs of a fuzzy system for each input. They are tailored for interpolative reasoning. Our approach to inference relies on the use of inferential independence. It is based on fuzzy output computation under an interval-valued input. A double decomposition of fuzzy inputs is done in terms of alpha-cuts and in terms of a partitioning of these cuts according to areas where only a few rules apply. The case of 1-D and 2-D inputs is considered, as well as higher dimensional cases. An application to a cheese-making process illustrates the approach.