Abstract: The concept of weighted regular metric is proposed in the unified framework of strong regular implication operators. The weighted fuzzy metric space is established based on strong regular implication operators and its properties are studied. Continuity of mappings corresponding to commonly used logic connectives is analyzed. Finally, it is proved that the weighted regular fuzzy metric space based on Lukasiewicz implication is most suitable for developing fuzzy reasoning.

Key words: fuzzy metric space, fuzzy reasoning, strong regular implication operator, weighted regular metric

摘要： 在强正则蕴涵算子的统一框架下给出了加权正则度量的定义，建立了基于强正则蕴涵算子的加权正则模糊度量空间，并且研究了该模糊度量空间的性质，分析了常用的逻辑连接词所对应的映射关于加权正则度量的连续性，最后证明了基于Lukasiewicz蕴涵的加权正则模糊度量空间是最适宜于展开模糊推理的模糊度量空间。

关键词: 模糊度量空间, 模糊推理, 强正则蕴涵算子, 加权正则度量