提出用区间值模糊测度刻画融合结果的置信范围,提升决策融合的可解释性。
Characterisation of Density-based FM generation methods in the context of Information Fusion

- 通过密度信息构建区间值模糊测度,解决传统方法参数不唯一问题
- 结合具体融合模型与数据集,得到更精确的区间测度
- 首次实现对理想融合结果的置信区间估计,适合高可靠性决策场景
基于模糊积分(FI)的聚合在集成学习与决策级融合中具有强大表达能力,其核心挑战在于模糊测度(FM)的合理参数化,需捕捉各组件及其组合的权重。现有方法如Sugeno-λ和可分解FM通过个体源的密度外推来定义FM,同时满足单调性约束。本文指出,仅凭密度信息通常不足以唯一确定离散FM;但可唯一确定一个区间值FM。进一步地,结合特定的FI模型与数据集,可获得更具体的区间值FM。实践中,评估经验确定的FM质量较为困难。为此,本文提出计算区间FM包含理想(即难以获取的最佳或真实)数值FM的似然性,从而在给定置信水平下生成置信区间。实验表明,基于该FM的Choquet FI输出可视为理想融合结果的置信区间,为事前表征融合结果提供了新方法,并指明了未来研究方向。
原文摘要 · Abstract (English)
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.
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