Approximation capability of SISO Fuzzy Relational Inference systems based on fuzzy implications

In this work, we show that fuzzy inference systems based on Fuzzy Relational Inference (FRI) with implicative interpretation of the rule base are universal approximators under suitable choice of operations for the rest of the components of the fuzzy system. The presented proofs make no assumption on the form or representations of the considered fuzzy implications and hence show that a much larger class of fuzzy implications other than what is typically considered in the literature can be employed meaningfully in FRIs based on implicative models.