Hyper effect algebras

We present hyper effect algebras as a generalization of effect algebras. The result of the hyper summation of two mutually excluding events is not an element of the algebra but rather a subset (not necessarily a singleton) of the algebra. We present basic notions like states on hyper effect algebras. We present two standard examples of hyper effect algebras starting from effect algebras. We show how we can effectively generate finite models of hyper effect algebras and we point out problems with associativity. Finally, we provide a representation of any finite linearly ordered hyper effect algebra.