Binary Fuzzy Measures and Choquet Integration for Multi-Source Fusion


Countless challenges in engineering require the intelligent combining (aka fusion) of data or information from multiple sources. The Choquet integral (ChI), a parametric aggregation function, is a well-known tool for multisource fusion, where source refers to sensors, humans and/or algorithms. In particular, a selling point of the ChI is its ability to model and subsequently exploit rich interactions between inputs. For a task with N inputs, the ChI has 2^N interaction variables. Therefore, the ChI becomes intractable quickly in terms of storage and its data-driven learning. Herein, we study the properties of an efficient to store, compute, and ultimately optimize version of the ChI based on a binary fuzzy measure (BFM). The BFM is further motivated by empirical observations in the areas of multi-sensor fusion and hyperspectral image processing. Herein, we provide a deeper understanding of the inner workings, capabilities and underlying philosophy of a BM ChI (BChI). We also prove that two fuzzy integrals, the ChI and the Sugeno integral, are equivalent for a BFM. Furthermore, only a small subset of BFM variables need be stored, which reduces the BChI to a relatively simple look up operation.




D. T. Anderson, M. A. Islam, R. King, N. H. Younan, J. R. Fairley, S. Howington, F. Petry, P. Elmore and A. Zare, "Binary Fuzzy Measures and Choquet Integration for Multi-Source Fusion," Intl. Conf. on Military Technologies 2017. 
Title = {Binary Fuzzy Measures and Choquet Integration for Multi-Source Fusion},
Author = {Derek T. Anderson and Muhammad Aminul Islam and Roger King and Nicolas H. Younan and Joshua R. Fairley and Stacy Howington and Frederick Petry and Paul Elmore and Alina Zare},
Booktitle = {Intl. Conf. on Military Technologies},
Year = {2017}