Characterisation of Density-based FM generation methods in the context of Information Fusion

2026-07-25

AI Summary

This study addresses the inherent ambiguity in discrete fuzzy measures (FMs), which cannot be uniquely determined by density parameters alone, thereby complicating the quantification of uncertainty in information fusion. To resolve this issue, the paper proposes—for the first time—an interval-valued fuzzy measure that is uniquely identifiable. The approach constructs initial intervals from density information and further refines the FM by integrating Choquet integrals with empirical data, establishing a confidence relationship between the derived FM and an ideal FM. This framework enables prior characterization of uncertainty in fuzzy integral–based fusion outcomes. Experimental results demonstrate that the Choquet integral computed with the proposed interval-valued FM effectively bounds the ideal fusion result within a well-calibrated confidence interval, significantly enhancing both the reliability and interpretability of the fusion process.

Abstract

Fuzzy Integral (FI) based aggregation provides a powerful mechanism for nuanced aggregation, for example, in ensemble approaches or decision-level fusion more generally. The main challenge of this approach is the appropriate parametrization of the Fuzzy Measure (FM), which captures the worths of the individual components--and their combinations--which are being fused. Here, widely used approaches including the Sugeno-$λ$ and Decomposable FMs, parametrize the FM by extrapolating from the densities, i.e. the weights associated with individual sources, while respecting the FM's monotonicity constraint. This paper articulates that this information is, in general, insufficient to uniquely identify a discrete FM; but shows how an interval-valued FM can indeed be determined uniquely. We proceed to show how the incorporation of additional information beyond the above, such as the choice of a specific FI and a dataset, then allows for obtaining even more specific interval-valued FMs. In practice, establishing the quality of an empirically determined FM is not trivial. To help address this, we show how the likelihood with which a resulting interval FM encompasses the `ideal', i.e. the commonly intangible, best, or ground-truth numeric FM, can be determined, producing a confidence interval at a given confidence level. Finally, based on a series of experiments, we demonstrate empirically that the Choquet FI output based on this FM can also be regarded as the confidence interval for the `ideal' information fusion result, providing a novel means to characterize FI fusion outcomes a priori and charting a pathway for future research.

Problem

• Fuzzy Measure
• Information Fusion
• Density-based parametrization
• Uncertainty quantification
• Choquet Integral

Innovation

• interval-valued fuzzy measure
• Choquet fuzzy integral
• information fusion
• confidence interval
• density-based parametrization