Robustness of full implication algorithms based on interval-valued fuzzy inference

•A new kind of full implication algorithm based on interval-valued fuzzy set is proposed.•The R-type triple I solutions based on interval-valued fuzzy reasoning are given.•The new triple I algorithms based on interval-valued fuzzy set are robust.•The sensitivity of some special algorithms based on four important interval-valued residuated implication is given.

In this paper, a new full implication algorithm based on interval-valued fuzzy inference which extends the triple I principle for fuzzy inference based on fuzzy modus ponens and fuzzy modus tollens to the case of interval-valued fuzzy sets is presented. We first give the corresponding interval-valued RR-type triple I solutions and then investigate the robustness of triple I algorithms based on interval-valued fuzzy sets for fuzzy inference. The sensitivity of some special algorithms based on four important interval-valued residuated implication is given. It is shown that the robustness of interval-valued full implication algorithms for fuzzy inference directly depends on the selection of interval-valued fuzzy connectives.