Uncertainty merging with basic uncertain information in probability environment

Basic uncertain information is a recently introduced and significant type of uncertainty that proves particularly valuable in decision-making environments with inherent uncertainties. In this study, we propose the concept of uncertainty cognition merging, which effectively combines basic uncertain information granules with probability measures to generate new probability measures within the same probability space. Additionally, we present a degenerated method that merges basic uncertain information granules with unit intervals to create new subintervals. We introduce four distinct uncertainty cognition merging methods and thoroughly compare and analyze their respective properties, limitations, and advantages. To demonstrate the practical application potential of our proposals, we provide numerical examples alongside further mathematical results.