This paper proposes the weaker axioms which admit a cardinal utility representation under ambiguity separating ambiguous beliefs from preferences in a purely subjective setting. The representation is obtained in an implicit form, which corresponds to the disappointment aversion utility (Gul, 1991) with respect to a non-additive measure in place of a probability measure. It includes all the properties of cardinality, ambiguity aversion, reference dependency, gain/loss asymmetry, and the distortion in probability evaluations. It enables us to capture varying attitude toward ambiguity such as Machina's examples (2009, 2014) in the simplest way.
