Evidence approach imprecise intervals: extensions and evaluation measures

In a number of applications the data will be represented in an interval format. We consider here a nested representation of uncertain information in intervals using Dempster-Shafer evidence approaches. These representations can be used in variety of applications including spatial and temporal reasoning and economic cost valuations. Two representations of nested intervals, RP1 and RP2, are defined and used in the paper. Basically an inner interval represents the more certain data and is nested in the outer less certain interval. We illustrate how the specificity measure could be used to evaluate such nested Dempster-Shafer intervals. We then consider Gini information measures applicable to the RP1 representation. We describe an example using our interval approach to COVID contact tracing in epidemiology. Finally examples of aggregation of intervals are provided. It is seen that an aggregated result can be evaluated and shown to increase the specificity of the result. Additionally, it is not always the case that aggregation increases specificity. An example is given illustrating such a case.