Abstract: Whether the (G,N) implication satisfies Modus Ponens, Modus Tollens, and Hypothetical Syllogism is discussed in this paper, and some criteria that (G,N)-the implication satisfies the corresponding inference rules under some common t-norms is given, which provides a reference for optimizing the design of fuzzy inference algorithm.

Key words: triangular norms, (G,N)-implication, Modus Ponens, Modus Tollens, Hypothetical Syllogism