Uncertain expected utility function and its risk premium

Other than traditional decision theory, this paper employs uncertainty theory to handle indeterminacy. uncertain variables are used to represent uncertain choices. uncertain expected utility function is defined as an increasing function of uncertain choices. several mathematical properties of the uncertain expected utility functions are derived using inverse uncertainty distributions. in order to compare two different choices, the first order dominance and second order dominance via uncertain expected utility functions are introduced. we also investigate risk aversion attitude and risk premium. finally, the relationship between risk premium and risk averse attitude is investigated.