值域为坡代数的加权图和模糊图的范畴关系

Categorical relations between weighted graphs and fuzzy graphs ranged in incline algebras

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。

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.