Fuzzy rules; Inference mechanism; Conditional firing

In [1], B. Moser and M. Navara defined three axioms for fuzzy inference systems and showed, that usually neither very popular Mamdani-Assilian nor logically motivated implicative fuzzy systems, do satisfy them simultaneously. Therefore, the authors introduced so-called conditionally firing rules and proved, that under very mild conditions, all three axioms may be satisfied simultaneously. However, the advantageous composition, which is directly related to the inference, is the direct image (related to CRI) when dealing with the implicative interpretation of fuzzy rules, and the subdirect image (related to BKS) when dealing with Mamdani-Assilian interpretation of fuzzy rules, not vice-versa. This article aims directly at this point and investigates the satisfaction of Moser-Navara axioms by the preferable combinations of rule interpretations and inference mechanisms.