中文摘要：

三I算法是一种新的模糊推理方法，是传统的模糊推理方法的修改争补充。三I表达式取最小值时的最优解算法（即对偶三I算法）是三I算法思想的延伸和完善。零文针对蕴涵算子族Ip，讨论了FMP和FMT问题的对偶三I算法，给出了相应的计算公式，从而也进一步促进了对三I算法的研究。

英文摘要：

The triple I method is a new kind of fuzzy reasoning method with respect to FMP and FMT reasoning models, and improves on the conventional fuzzy reasoning methods. As far as dual form of triple I method is concerned, it extends and perfects the idea of triple I method. In this paper, based on a class of residual implications, the corresponding formula of the optimal solutions as dual form of triple I method are obtained. All these obtained results will be very helpful to study the Triple I method.