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.

翻译：模糊推理引擎作为模糊系统最重要的组成部分之一，能够利用模糊逻辑推理方法，从输入空间上的模糊集和模糊规则库中获取有意义的输出。为提高多输入单输出(MISO)模糊系统中模糊推理引擎的计算效率，本文主要研究基于满足聚合函数输入律(LIA)的模糊蕴涵的三种MISO模糊分层推理引擎。首先，我们针对已知的模糊蕴涵找出部分满足(LIA)的聚合函数。随后，对于给定的聚合函数，刻画了与其满足(LIA)的模糊蕴涵特征。最后，应用上述理论成果，在MISO模糊系统中构建了三种模糊分层推理引擎。