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.



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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.



Terminology for generalized relations
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. 


