  Fuzzy inference engine, as one of the most important components of fuzzy
systems, can obtain some meaningful outputs from fuzzy sets on input space and
fuzzy rule base using fuzzy logic inference methods. In order to enhance the
computational efficiency of fuzzy inference engine in
multi-input-single-output(MISO) fuzzy systems,this paper aims mainly to
investigate three MISO fuzzy hierarchial inference engines based on fuzzy
implications satisfying the law of importation with aggregation functions
(LIA). We firstly find some aggregation functions for well-known fuzzy
implications such that they satisfy (LIA). For a given aggregation function,
the fuzzy implication which satisfies (LIA) with this aggregation function is
then characterized. Finally, we construct three fuzzy hierarchical inference
engines in MISO fuzzy systems applying aforementioned theoretical developments.
