Axiomatic analysis of total uncertainty measures for belief functions and non-additive uncertainty models

Total uncertainty measures for belief functions arise from different conceptual principles and are used in evidence-based applications. However, the selected measures have not been systematically assessed under a common framework with respect to informational monotonicity, independent composition, and marginalisation. This paper analyses maximum entropy over the credal set, the pignistic ambiguity measure, Deng entropy, several Deng-type extensions, and a belief–plausibility interval entropy. Previously established results are distinguished from new analyses and counterexamples. Maximum entropy satisfies monotonicity, additivity, and subadditivity. Deng entropy, the Zhou and Cui extensions, the analysed W entropy with ε=1, and the belief–plausibility interval entropy fail all three properties, whereas the pignistic ambiguity measure satisfies only additivity. Measures based on different constructions may therefore violate the same coherence requirements, even for simple evidence structures. The analysis provides theoretical criteria for selecting uncertainty measures and motivates subsequent empirical and computational evaluation in data-mining applications.