An Uncertainty Measure With Monotonicity Under the Random Set Inclusion

In the setting of the theory of evidence, we propose a new uncertainty measure which can capture, in modeling a situation including uncertainty, two different kinds of uncertainty: one is what is measured by the Shannon entropy and another is related to cardinality. Our proposed measure is a generalization of the Shannon entropy and monotonic with respect to random set inclusion. Its properties are investigated and its potentiality is illustrated with an example.