On continuity of the entropy-based differently implicational algorithm

Aiming at the previously-proposed entropy-based differently implicational algorithm of fuzzy inference, this study analyzes its continuity.To begin with, for the FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems, the continuous as well as uniformly continuous properties of the entropy-based differently implicational algorithm are demonstrated for the Tchebyshev and Hamming metrics, in which the R-implications derived from left-continuous tnorms are employed.Furthermore, four numerical fuzzy inference examples are provided, and it is found that the entropy-based differently implicational algorithm can obtain more reasonable solution in contrast with the fuzzy entropy full implication algorithm.Finally, in the entropybased differently implicational algorithm, we point out that the first fuzzy implication reflects the effect of rule base, and that the second fuzzy implication embodies the inference mechanism.