Interval-valued quintuple implication principle of fuzzy reasoning

In this paper, we propose the quintuple implication principle based on interval-valued fuzzy inference for fuzzy modus ponens and fuzzy modus tollens, which explicitly use the closeness between A⁎ and A (or B⁎ and B) in the process of fuzzy reasoning. We first give the corresponding interval-valued R-type quintuple implication solutions and then investigate the robustness of quintuple implication algorithms based on interval-valued fuzzy inference. The sensitivity of quintuple implication algorithms based on two important interval-valued residuated implication operators is given.