反向三I算法的连续性和误差传播

Continuity properties and error propagation of reverse triple-implication method of fuzzy reasoning

对全蕴涵反向三I算法是否满足连续性问题进行了首次研究,并进一步讨论了这类算法对误差的传播性能.文中把模糊推理算法看成是一个模糊集合到另一个模糊集合的映射,选用海明距离作为两模糊集的距离,证明了在模糊假言推理和模糊拒取式推理情形,该算法都拥有连续性;其对误差的放大幅度为2.

We investigate the continuity properties of the implicit reverse triple-implication algorithm;and discuss in depth the error propagation in this type of algorithm.A fuzzy inference algorithm is viewed as a mapping from one fuzzy set to the other fuzzy set;the distance between them is computed by the Hamming distance formula.We prove that the algorithm holds continuity properties in the case of fuzzy modus ponens and fuzzy modus tollendo ponens.In both cases,the magnification factor for the errors is 2.