Fuzzy Integral = Contextual Linear Order Statistic
This work addresses the challenge of making fuzzy integrals more scalable and interpretable for applications in information fusion, classification, and decision making, though it appears incremental as it builds on existing concepts.
The paper tackled the problem of representing the fuzzy integral, a nonlinear operator, as a set of contextual linear order statistics, enabling scalability, improved acquisition, generalizability, and interpretability. The methods were validated on synthetic experiments and real-world benchmark datasets.
The fuzzy integral is a powerful parametric nonlin-ear function with utility in a wide range of applications, from information fusion to classification, regression, decision making,interpolation, metrics, morphology, and beyond. While the fuzzy integral is in general a nonlinear operator, herein we show that it can be represented by a set of contextual linear order statistics(LOS). These operators can be obtained via sampling the fuzzy measure and clustering is used to produce a partitioning of the underlying space of linear convex sums. Benefits of our approach include scalability, improved integral/measure acquisition, generalizability, and explainable/interpretable models. Our methods are both demonstrated on controlled synthetic experiments, and also analyzed and validated with real-world benchmark data sets.