Combining nonspecificity measures in Dempster–Shafer theory of evidence

Abstract

In Dempster–Shafer theory (DST) of evidence coexist two types of uncertainty: conflict and nonspecificity. The maximum of entropy is a total uncertainty measure that verifies an important set of properties in this theory. We prove that this function has a fault of sensibility to changes in evidence in situations where only the part of nonspecificity is presented in the uncertainty (uncertainty without conflict), producing no-logical values. We analyse two measures of nonspecificity presented in DST, which have been used as part of total uncertainty measures. We compare their behaviour, focusing on situations where only the part of nonspecificity is presented in the uncertainty. We will see that it makes sense to combine them and use this combination as part of a total uncertainty measure verifying an important set of properties and behaviours. This new total measure has not the mentioned problem of lack of sensitivity to changes in evidence.