Abstract: It is different from that the usual similarity degree is defined based on truth degree, this paper puts forward the integral similarity degree by use of S-implication operator in S- implication fuzzy logic system. Then the paper discusses the relationship between integral similarity and logical equivalence, gives the inference properties of the integral similarity degree, proposes the pseudo-metric corresponding to the integral similarity degree. The continuity of the logical operators in pseudo-metric space is proved.

Key words: S-logic system, integral similarity degree, pseudo-metric

摘要： 与通常相似度定义在真度基础上不同，在S-蕴涵模糊逻辑系统中提出了基于S-蕴涵算子的积分相似度。讨论了积分相似与逻辑等价的关系，给出了积分相似度的推理性质，提出了与积分相似度对应的伪距离。论证了伪距离空间中逻辑算子都是连续的。

关键词: S-逻辑系统, 积分相似度, 伪距离