A practical inference method with several implicative gradual rules and a fuzzy input: one and two dimensions

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 α-cuts and in terms of a partitioning of these cuts according to areas where only a few rules apply. The case of one and two dimensional inputs is considered.