In order to capture a larger range of decision rules, this paper extends the seminal work of [Friedman and Halpern, 1995, Chu and Halpern, 2003, 2004] about Generalized Expected Utility. We introduce the notion of algebraic mass function (and of algebraic Möbius transform) and provide a new algebraic expression for expected utility based on such functions. This utility, that we call “XEU”, generalizes Chu and Halpern’s GEU to non-decomposable measures and allows for the representation of several rules that could not be captured up to this point, and noticeably, of the Choquet integral. A representation theorem is provided that shows that only a very weak condition is needed for a rule in order to be representable as an XEU.