Generating random fuzzy (capacity) measures for data fusion simulations

Document Type

Conference Proceeding

Publication Date

2-8-2018

Department

Department of Electrical and Computer Engineering; Center for Data Sciences

Abstract

The fuzzy integral (FI) with respect to a fuzzy measure (FM) is a powerful means of aggregating information. The most popular FIs are the Choquet and Sugeno and most research focuses on these two variants; here, we focus on the Choquet. The arena of the FM is much more populated, including numerically-derived FMs such as the Sugeno λ-measure and decomposable measure, expert-defined FMs, and data-informed FMs. This paper fills a gap in the research on FMs and FIs by proposing three ways to randomly generate FMs with an emphasis on appropriately filling the space of all possible FMs and the way in which they interact with the Choquet FI. The methods proposed here provide a useful simulation tool that can be used for developing and testing FM-learning methods, for testing FM-based aggregation and fusion, and for gaining a better understanding about the space of FMs and how to exploit that space for better application or learning. To facilitate discussion of our random FM generators, we also develop a visualization tool for the Choquet FI, with respect to a FM, called a C g -plot. This tool allows Choquet FI users to visualize the operations that the Choquet FI is performing for a given FM. Lastly, we compare the three FM generators and make recommendations regarding their use.

Publisher's Statement

©2017 IEEE. Publisher's version of record: https://doi.org/10.1109/SSCI.2017.8285272

Publication Title

2017 IEEE Symposium Series on Computational Intelligence

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