Monotonicity of Entropy Computations in Belief Functions

This article addresses the issue of quantitative information measurement within the Dempster--Shafer belief function formalism. Entropy computation in Dempster--Shafer depends on the way uncertainty measures are conceptualized. However, freed of most probability constraints, uncertainty measures in Dempster--Shafer theory can lead to further advances in optimization in information theory, which in turn may have a wide impact on decision and control. This article examines one form of current development regarding the entropy measure induced from the measure of dissonance. For a significant period, the measure of dissonance has been taken as a measure of entropy. We present in this article the entropy measure as a monotonically decreasing function, symmetrical to the measure of dissonance.