Dempster-Shafer theory and connections to Choquet's theory of capacities and information theory

Abstract

The axiomatic development of information theory, during the 1960's, led to the discovery of various composition laws. The Wiener-Shannon law is well understood, but the Inf law holds particular interest because it creates a connection with the Dempster-Shafer theory. Proceeding along these lines, in a previous paper, I demonstrated the connection between the Dempster-Shafer theory and Information theory. In 1954, Gustave Choquet developed the theory of capacities in connection with potential theory. The basic concepts of capacity theory arise from electrostatics, but a capacity is a generalization of the concept of measure in Analysis. It is well known that Belief and Plausibility in the Dempster-Shafer theory are Choquet capacities. However, it is not well known that the inverse of an information measure is a Choquet capacity. The objective of this paper is to demonstrate the connections among the Dempster- Shafer theory, Information theory and Choquet's theory of capacities.