Interval Agreement Weighted Average - Sensitivity to Data Set Features

The growing use of intervals in fields like survey analysis necessitates effective aggregation methods that can summarize and represent such uncertain data representations. The Interval Agreement Approach (IAA) addresses this by aggregating interval responses into Fuzzy Sets (FSs), capturing both intra- and inter-participant agreement, while minimizing information loss. While offering a powerful modeling tool, the IAA does not natively offer a measure of central tendency, which is itself an interval of particular utility in real-world applications. In contrast, the Interval Weighted Average (IWA) has been used for directly measuring the central tendency of intervals. While straightforward and effective, it is not designed, nor able to, summarize interval data in terms of their agreement, as the IAA does. To bridge this gap, this paper introduces Interval Agreement Weighted Average (IAWA), which is specifically designed to reflect both the central tendency and agreement. This is achieved by first modeling interval agreement as FSs using the IAA, and then transforming these FSs into intervals using the IWA. We demonstrate the approach by conducting sensitivity analyses to explore the behavior of the proposed approach in detail. Our findings suggest that the IAWA is a highly effective measure of central tendency. Additionally, it also partially inherits IAA's ability to reflect the agreement of sets of intervals. We conclude by highlighting the potential and growth of the use of intervals in information elicitation, within, and beyond survey research, underpinning a new degree of understanding of both intra- and inter-source uncertainty.