CRI as approximate reasoning tool: an analysis via T-indistinguishability operators

The compositional rule of inference (CRI) is a useful tool for doing approximate reasoning in the sense that similar hypothesis are transformed via CRI into similar thesis. In the paper we formalize the meaning of these similarities by means of the natural T-indistinguishability E~ (an indistinguishability operator over a set of fuzzy sets). We prove that all the CRI processes are extensional with respect to E~ independently of the fuzzy relation used to model the implication (Residuated, Mamdani, ...). Finally, we propose a new inference operator, different from the CRI, termed the natural inference operator that is optimal from the extensional point of view.