Some general fusion and transformation frames for merging basic uncertain information

The Basic Uncertain Information (BUI) is a recently introduced type of uncertain data that has rapidly undergone development and practical application. The existing aggregation operators designed for BUI solely encompass the weighted mean and Choquet integral. The present study puts forth a set of general information fusion frameworks and methodologies aimed at gathering BUI granules. The first mode yields BUI granules as its output, whereas the subsequent two modes generate outputs in the form of interval values. The paper includes numerical examples and applications that correspond to the presented findings. The present study conducts an analysis of various mathematical properties pertaining to the three BUI fusion modes that have been proposed. These properties include idempotency, monotonicities, certainty derived inclusion, certainty monotonicity, homogeneities, non-symmetricity, comonotone additivities, and continuities. The proposals and analyses presented in this work are of a general nature and have the potential to inspire various practical specifications.