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

MISO hierarchical inference engine satisfying the law of importation with aggregation functions