Binary fuzzy measures and Choquet integration for multi-source fusion

• Published in: 2017 International Conference on Military Technologies (ICMT) pp. 676 - 681
• Main Authors: Anderson, Derek T., Islam, Muhammad Aminul, King, Roger, Younan, Nicolas H., Fairley, Joshua R., Howington, Stacy, Petry, Frederick, Elmore, Paul, Zare, Alina
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-05-2017
• Subjects: binary Choquet integral; binary fuzzy measure; Choquet integral; Frequency modulation; fuzzy measure; Hyperspectral sensors; Lattices; multi-sensor fusion; Sensor fusion; Silicon
• DOI: 10.1109/MILTECHS.2017.7988843

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 multi-source 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 BFM 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.