Approximate reasoning with aggregation functions satisfying GMP rules.

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