Abstract: Fuzzy reasoning is the core of fuzzy control, the reversibility is one of most important evaluation stan- dards for fuzzy reasoning algorithms. Under the framework of regular implication operators, this paper firstly gives the unified expression for solving FMP (fuzzy modus ponens) problems based on SIS (subsethood infer subsethood) method. Secondly, this paper proposes an improved SIS FMT (fuzzy modus tollens) algorithm and the unified form of its solution. In the end, this paper proves that the SIS FMP algorithm and SIS FMT algorithm are both unconditionally reversible, and studies the λ-solution of SIS algorithm for FMP and FMT. This algorithm will provide more alternative methods of fuzzy reasoning for the area of fuzzy control.

Key words: fuzzy control, fuzzy reasoning, regular implication operators, SIS algorithm

摘要： 模糊推理是模糊控制的核心问题，还原性则是评价模糊推理算法好坏的重要标准之一。在正则蕴涵算子的统一框架下，给出了基于模糊推理SIS（subsethood infer subsethood）算法的模糊取式（fuzzy modus ponens，FMP）问题解的统一表达式；基于SIS算法为模糊拒取式（fuzzy modus tollens，FMT）问题提出了一种改进的求解原则，并给出了FMT问题解的统一形式；证明了SIS FMP算法和SIS FMT算法均满足无条件还原性，讨论了FMP问题及FMT问题基于SIS算法的λ-水平解。该算法将为模糊控制领域提供更多可供选择的模糊推理方法。

关键词: 模糊控制, 模糊推理, 正则蕴涵算子, SIS算法