在Quantale中引入模糊滤子的概念,研究了它的一系列性质,得到了若干等价刻画,讨论了Quantale中滤子和模糊滤子之间的相互确定关系,证明了Quantale态射既保模糊滤子又反射模糊滤子。给出了模糊滤子在Quantale态射下的像的具体结构。
In this paper, the notion of fuzzy filters in quantales is introduced and its natures are studied. Some equivalent characteristics of fuzzy filters are given and the relationships between filters and fuzzy filters are discussed. It is proved that quantic morphisms preserve and reflect fuzzy filters and the concrete structures of the image of fuzzy filters on quantic morphisms are obtained.