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Interval-valued fuzzy reasoning plays a vital role in intelligent systems with the performance of effectively reducing the loss of fuzzy information and reflecting the vagueness and uncertainty in information processing. However the existing reasoning algorithms were developed based on some special interval-valued t-norms which limits the usability and adaptation of these algorithms. This study proposes general reasoning algorithms on the basis of interval-valued fuzzy sets, that is the interval-valued fuzzy reasoning triple I algorithms based on the left-continuous t -representable t -norm T T 1 , T 2 . Furthermore, the interval-valued R -type triple I solutions of the interval-valued fuzzy reasoning triple I algorithms are given. We show that the proposed algorithms possess the reducibility. Finally, some robustness results of the interval-valued fuzzy reasoning triple I algorithms based on the left-continuous interval-valued t -representable t -norm are proved. [ABSTRACT FROM AUTHOR]