  To strengthen the effectiveness of approximate reasoning in fuzzy modus
ponens (FMP) and fuzzy modus tollens (FMT) problems, three approximate
reasoning schemes with aggregation functions are developed and their validity
is respectively investigated in this paper. We firstly study some properties of
fuzzy implication generated by aggregation function. And then present an
$A$-compositional rule of inference (ACRI) as an extension of Zadeh's CRI
replacing $t$-norm by an aggregation function. The similarity-based approximate
reasoning with aggregation functions is further discussed. Moreover, we provide
the quintuple implication principle (QIP) method with aggregation functions to
solve FMP and FMT problems. Finally, the validity of our proposed three
approximate reasoning approaches is respectively analyzed using GMP rules in
detail.
