AI 中文总结
研究信息融合中基于密度的FM生成方法，指出常用方法不足以唯一确定离散FM，展示如何确定区间值FM及相关置信区间，通过实验表明基于此FM的Choquet FI输出可视为‘理想’融合结果置信区间，为表征FI融合结果提供新途径。
AI 中文摘要
基于模糊积分（FI）的聚合为细微聚合提供了强大机制，例如在集成方法或决策级融合中。该方法的主要挑战是模糊测度（FM）的适当参数化，它捕捉融合的各个组件及其组合的价值。常用方法通过从密度外推来参数化FM，但一般不足以唯一确定离散FM，本文表明区间值FM可唯一确定，纳入更多信息可得到更具体的区间值FM。实践中确定经验FM的质量不易，本文展示了如何确定区间FM包含‘理想’FM的可能性及置信区间。基于实验表明基于此FM的Choquet FI输出可视为‘理想’信息融合结果的置信区间，为表征FI融合结果提供新方法并为未来研究指明方向。
英文摘要
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.
