Evidence approach imprecise intervals: extensions and evaluation measures.

Area of Science:

• Uncertainty Quantification
• Evidence Theory
• Data Representation

Background:

• Data is often represented in interval formats, requiring methods to handle uncertainty.
• Dempster-Shafer theory provides a framework for reasoning with uncertain information.
• Nested interval representations offer a way to structure uncertain data with varying degrees of certainty.

Purpose of the Study:

• To define and explore nested interval representations (RP1 and RP2) for uncertain information using Dempster-Shafer evidence theory.
• To evaluate the specificity of these nested intervals using specificity and Gini information measures.
• To demonstrate the application of these interval approaches in areas such as COVID contact tracing and data aggregation.

Main Methods:

• Definition of two nested interval representations, RP1 and RP2, where inner intervals represent more certain data.
• Application of specificity measures to evaluate the nested Dempster-Shafer intervals.
• Utilization of Gini information measures for the RP1 representation.
• Demonstration of interval aggregation techniques and their impact on specificity.

Main Results:

• Nested Dempster-Shafer intervals can be evaluated using specificity measures.
• Gini information measures are applicable to the RP1 representation.
• Aggregation of intervals can increase specificity, but this is not always guaranteed.
• A COVID contact tracing example illustrates the practical application of the interval approach.

Conclusions:

• Nested interval representations provide a robust method for handling uncertain data within Dempster-Shafer frameworks.
• Specificity and Gini measures are effective tools for evaluating the information content of these nested intervals.
• The aggregation of uncertain interval data can enhance result specificity, though careful consideration of specific cases is necessary.