Monotonicity of Entropy Computations in Belief Functions

Article type: Research Article

Authors: Maluf, David A.^{; 1}

Affiliations: Department of Computer Science, Stanford University, Palo Alto, CA 94305, USA

Note: [1] E-mail: [email protected].

Abstract: 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.

Keywords: Belief functions, Dempster–Shafer theory, Entropy measure, Uncertainty measure, Measure of dissonance

DOI: 10.3233/IDA-1997-1305

Journal: Intelligent Data Analysis, vol. 1, no. 3, pp. 207-213, 1997