Abstract: Inclines are additively idempotent semirings in which products are less than or equal to either factor. For an idempotent semiring as the codomain, this paper shows that the category of weighted graphs can be simultaneously embedded in the category of fuzzy graphs as a reflective and coreflective subcategory.

Key words: incline algebra, weighted graph, fuzzy graph, （co）reflective subcategory

摘要： 坡代数是元素的乘法小于等于每个因子的加法幂等的半环。以坡代数为取值域，证明了加权图范畴可以作为余反射子范畴嵌入到模糊图范畴中去；如果坡代数的乘法有单位元，则这种嵌入还具有反射性。

关键词: 坡代数, 加权图, 模糊图, （余）反射子范畴