On the Potential of Fuzzy Integral-based Decision-level Fusion when the Fuzzy Measure is Informed by Densities Alone

Aggregation is key technique in decision-level fusion of classifiers. Beyond affording performance in an ensemble-sense, such aggregation operator based fusion also has the potential to add a substantial layer of interpretability to the overall systems. This is particularly relevant when the individual classifiers focus on human-accessible features such as color, texture and shape in a computer vision setting. The fuzzy integral (FI) is a powerful aggregation method enabling the combination of evidence in respect to the worth of all possible combinations of sub-sources, encoded in a fuzzy measure (FM). The primary challenge of using FI is the appropriate configuration of the FM. Here, the Sugeno λ-FM is a very commonly used approach in decision-level fusion of classifiers, deriving a FM directly from the 'worth' of individual sources, i.e. the densities, and the FM's monotonicity constraint. While broadly adopted, it is not clear when and to what degree the resulting FMs enable the FI to deliver performance increases vs other, simpler aggregation operators such as even the average and weighted average. This paper investigates the latter as part of a decision-level fusion context, showing that indeed, the FI based on the Sugeno λ-FM does not necessarily afford improved performance. Through a series of experiments combining deep-learning classifiers with FI-based decision-level fusion, we provide an initial demonstration when this is the case, highlighting that the adoption of the FI as a decision-level fusion operator is a non-trivial choice. We conclude by discussing limitations and charting the steps for future work on enhanced parametrization of the FM for high-performance, explainable decision-level fusion.