Analyzing properties of Deng entropy in the theory of evidence

The theory of Evidence, or Shafer-Dempster theory (DST), has been widely used in applications. The DST is based on the concept of a basic probability assignment. An important part of this theory is the quantification of the information-based-uncertainty that this function represents. A recent measure of uncertainty (or information) in this theory, called the Deng entropy, has appeared as an interesting alternative to the measures presented so far. This measure quantifies the both types of uncertainty found in DST, then it is considered as a total uncertainty measure (TU). It is shown that this measure does not verify some of the essential properties for a TU in DST such as monotonicity, additivity and subadditivity. Also, the definition of this new measure produces other debatable situations. These shortcomings call in question the utility of this measure in applications.