<p>Fuzzy measure, also referred to as a monotonic measure, proves to be a powerful tool for describing the value of the uncertain variable. Its effectiveness stems from the accommodation of many uncertainties, including probabilistic, possibilistic, and epistemic, due to their relaxed constraints. However, measure-based uncertainty has not been widely developed due to difficulties in agreeing with other theories in modeling and handling uncertainty. In this paper, we develop the construction and processing approaches for measure-based uncertainty utilizing the Dempster-Shafer structure. In the realm of uncertainty modeling, the t canonical decomposition operates on fuzzy measures and offers an interpretable construction approach, which boasts more convenient interfaces for both knowledge and data. In the realm of uncertainty handling, the conjunctive and disjunctive combination rules of Dempster-Shafer granules are extended to handle measure-based uncertainty, thereby achieving information processing consistency across various uncertainty frameworks.</p>