Terminology for generalized relations I have a simple terminology request: recall that given sets $A$ and $B$, a relation $R$ from $A$ to $B$ is any subset of the product $A \times B$. Thus, one may view a relation as a function $A \times B \to \lbrace 0,1 \rbrace$ where $(a,b)$ maps to $1$ if and only if it lies in $R$.
What I'm looking for is the suitable adjective to describe the situation where $A \times B$ maps into a more general ordered space, like say $\mathbb{R}^+$. The "relation" in this case is not just a yes/no binary affair, but rather a ranking of some sort.

Is there a standard terminology for such a situation?

I thought of using ordered relation, but that is dangerous because it causes immediate confusion with order relation. Sorry for the possibly silly question, but I have been searching textbooks and internet for a few days with no luck. It seems likely that someone in set theory or combinatorics has named and used this type of relation before. Thank you for the help.
 A: This is called an $L$-valued relation, when $L$ is the target of the function, which can be viewed as the collection of possible truth values. 
Thus, a $2$-valued relation is just an ordinary relation of classical logic, where every instance has truth value either true or false. But for any Boolean algebra $\mathbb{B}$ we have $\mathbb{B}$-valued relations, which arise throughout forcing, or more generally with a Heyting algebra, or an $[0,1]$-valued relation, as in fuzzy logic. 
A: I'm not sure if there is a name for situations like $\mathbb{R}^{+}$, but if your ordered space is a Heyting algebra, then it's still just called a relation.  
The notion of a relation makes sense in any category with finite products, even when the objects don't have an underlying set structure.  A relation from $A$ to $B$ is just a subobject of $A\times B$.  In a topos, the subobjects of $A\times B$ are in one-to-one correspondence with morphisms from $A\times B$ to the subobject classifier $\Omega$, which is an internal (complete) Heyting algebra.
