There are two generalizations of usual groups: groupoids, where the multiplication operation becomes "partial", and hypergroups, for which the result of multiplying two elements is a probability measure rather than a single element. I am interested in the structure combining both these features (it might have been called "hypergroupoid", but apparently this term is already in use): multiplication is partial and obeys the same rules as in a groupoid, but its result is a probability measure on morphisms with the appropriate source and target objects. Any references?



Groupoids and hypergroups
Yes, the notion of hypergroupoids exits. See the following preprints:


<http://arxiv.org/abs/1403.3424>


<http://arxiv.org/abs/1402.0072>


Both the articles are published. The second article defines Haar systems for a locally compact hypergroupoids explains construction of $C^\*$-algebra of a hypergroupoid equipped with a Haar system. It also proves the disintegration theorem for hypergroupoids.


