Continuity of triple I methods based on several implications

Abstract

This paper focuses on the continuity problem of fully implicational triple I methods for fuzzy reasoning. Based on the residual implications generated by continuous triangular norms, the residual implication generated by nilpotent minimum with the standard negation and the Zadeh implication, respectively, continuity and uniform continuity properties of triple I methods are examined in Hamming and uniform metrics. We also investigate the continuity of the model of a fuzzy if-then rule corresponding to the triple I methods.