Fuzzy Integral = Contextual Linear Order Statistic

• URL: http://arxiv.org/abs/2007.02874v2
• Date: Tue, 20 Oct 2020 18:45:49 GMT
• Title: Fuzzy Integral = Contextual Linear Order Statistic
• Authors: Derek Anderson, Matthew Deardorff, Timothy Havens, Siva Kakula, Timothy Wilkin, Muhammad Islam, Anthony Pinar, and Andrew Buck
• Abstract summary: The fuzzy integral is a powerful parametric nonlin-ear function with utility in a wide range of applications. We show that it can be represented by a set of contextual linear order statistics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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