Abstract
Fuzzy Integral (FI) based aggregation provides a powerful mechanism for nuanced aggregation, particularly in ensemble approaches or decision-level fusion. 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—being fused.
Here, widely used approaches including Sugeno-$\lambda$ 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; however, it 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, 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 empirically demonstrate 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.
Blogger's Review: This paper provides significant insights into the parameterization of fuzzy measures in the context of fuzzy integrals for information fusion, particularly in how additional information can improve result accuracy. It paves the way for future research and is worth paying attention to.