Dechao Li

As the two basic fuzzy inference models, fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) have the important application in artificial intelligence. In order to solve FMP and FMT problems, Zadeh proposed a compositional rule of inference (CRI) method. This paper aims mainly to investigate the validity of A-compositional rule of inference (ACRI) method, as a generalized CRI method based on aggregation functions, from a logical view and an interpolative view, respectively. Specifically, the modus ponens (MP) and modus tollens (MT) properties of ACRI method are discussed in detail. It is shown that the aggregation functions to implement FMP and FMT problems provide more generality than the t-norms, uninorms and overlap functions as well-known the laws of T-conditionality, U-conditionality and O-conditionality, respectively. Moreover, two examples are also given to illustrate our theoretical results. Especially, Example 6.2 shows that the output B' in FMP(FMT) problem is close to B(DC) with our proposed inference method when the fuzzy input and the antecedent of fuzzy rule are near (the fuzzy input near with the negation of the seccedent in fuzzy rule).

To make a better application of I-transitive fuzzy relations and fuzzy preference relations in uncertainty reasoning and decision-making according to the practical requirement, it is meaningful to investigates the preservation of well-known properties when some I-transitive and fuzzy preference relations are aggregated, respectively. Therefore, this paper firstly characterize the aggregation functions in order to preserve some properties of I-transitive fuzzy relations. Further, two aggregation functions are constructed to preserve some relevant properties of fuzzy preference relations. Especially, focused on the T-S consistency, we further investigate the retainment of some T-S consistent fuzzy preference relations aggre-gated.

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.

We establish a new combinatorial identity related to the well-known Bernoulli numbers, which generalizes the result due to Feng and Wang. By means of the identity, we find a recursive formula for successively determining the coefficients of Ramanujan's asymptotic expansion for the generalized harmonic numbers.