A new approach for imprecise probabilities

This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of sub--weak complementation, denoted by ψ, which assigns to each event H a corresponding event of indecisive eventualities. Interval probability measures for an event H can then be defined by taking into account its set of indecisive eventualities, which is contained in the standard complement H^{c}. We characterize a broad class of interval probability measures and define their properties. Additionally, the interval distribution of a random variable is formulated, and a corresponding definition of stochastic dominance between two random variables is introduced. As a byproduct, a formal solution to the century-old Keynes-Ramsey controversy is presented.