Fuzzy conditional inference under max-⊙ composition

This paper shows that the majority of fuzzy inference methods for a fuzzy conditional proposition “If x is A then y is B,” with A and B fuzzy concepts, can infer very reasonable consequences which fit our intuition with respect to several criteria such as modus ponens and modus tollens, if a new composition called “max-⊙ composition” is used in the compositional rule of inference, though reasonable consequences cannot always be obtained when using the max-min composition, which is used usually in the compositional rule of inference. Furthermore, it is shown that a syllogism holds for the majority of the methods under the max-⊙ composition, though they do not always satisfy the syllogism under the max-min composition.