We extend the $\alpha$ and $\beta$ characteristic functions (CFs) to cooperative interval games, which constitute an interesting class of games to account for uncertainty and vagueness in decision-making processes. Both characteristic functions are based on a solution of zero-sum interval games when a coalition is the maximizer player and the anti coalition is the minimizer player. We propose an algorithm to define the interval values of a cooperative game in the form of $\alpha$ and$\beta$ CFs and demonstrate them on an example of a three-person game. Further, we discuss some properties of cooperative interval games and calculate an interval Shapley value. Numerical examples show that the cooperative solution depends on the way we construct a CF to define a cooperative interval game.