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 weak complementation denoted as psi. The interval probability measure of an event H is defined with respect to the set of indecisive eventualities (psi(H))c, which is included in the standard complement Hc. We characterize a broad class of interval probability measures and define their properties. Additionally, we establish an updating rule with respect to H, incorporating concepts of statistical independence and dependence. 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.