On robustness of the full implication triple I inference method with respect to finer measurements

•We compare various perturbations or similarity degrees, which induced by different kinds of measures, between two fuzzy sets.•Finer measures for appraising robustness of fuzzy reasoning are proposed.•We present robustness of logic connectives and triple I method with respect to finer measurements.•Continuity of triple I method based on the finer measures is proved.

This paper mainly discusses three points. First of all, different types of equalities and similarity degrees between two fuzzy sets on a given universe of discourse are compared and analyzed. In particular, the concept of (T,δ)(T,δ) equality is revised as a measure to evaluate robustness of fuzzy reasoning. Besides, several induced metrics with respect to left-continuous T-norms are investigated, and properties of the related metric spaces are discussed. Finally, based on discussions above, the continuity of the triple I method with respect to the revised measures is proved, which reflects the good behavior of robustness of the triple I method.