The arithmetic recursive average as an instance of the recursive weighted power mean

Wagner, Christian; Havens, Timothy C.; Anderson, Derek T.

Abstract

The aggregation of multiple information sources has a long history and ranges from sensor fusion to the aggregation of individual algorithm outputs and human knowledge. A popular approach to achieve such aggregation is the fuzzy integral (FI) which is defined with respect to a fuzzy measure (FM) (i.e. a normal, monotone capacity). In practice, the discrete FI aggregates information contributed by a discrete number of sources through a weighted aggregation (post-sorting), where the weights are captured by a FM that models the typically subjective ‘worth’ of subsets of the overall set of sources. While the combination of FI and FM has been very successful, challenges remain both in regards to the behavior of the resulting aggregation operators—which for example do not produce symmetrically mirrored outputs for symmetrically mirrored inputs—and also in a manifest difference between the intuitive interpretation of a stand-alone FM and its actual role and impact when used as part of information fusion with a FI. This paper elucidates these challenges and introduces a novel family of recursive average (RAV) operators as an alternative to the FI in aggregation with respect to a FM; focusing specifically on the arithmetic recursive average. The RAV is designed to address the above challenges, while also facilitating fine-grained analysis of the resulting aggregation of different combinations of sources. We provide the mathematical foundations of the RAV and include initial experiments and comparisons to the FI for both numeric and interval-valued data.

Citation

Wagner, C., Havens, T. C., & Anderson, D. T. (2017). The arithmetic recursive average as an instance of the recursive weighted power mean. In 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (1-6). https://doi.org/10.1109/FUZZ-IEEE.2017.8015507

• Conference Name: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2017)
• Start Date: Jul 9, 2017
• End Date: Jul 12, 2017
• Acceptance Date: Mar 14, 2017
• Online Publication Date: Aug 24, 2017
• Publication Date: 2017
• Deposit Date: Apr 26, 2017
• Publicly Available Date: Aug 24, 2017
• Journal: Proceedings of the IEEE International Fuzzy Systems Conference
• Electronic ISSN: 1544-5615
• Peer Reviewed: Peer Reviewed
• Pages: 1-6
• Series ISSN: 1558-4739
• Book Title: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• ISBN: 978-1-5090-6035-1
• DOI: https://doi.org/10.1109/FUZZ-IEEE.2017.8015507
• Public URL: https://nottingham-repository.worktribe.com/output/878866
• Publisher URL: http://ieeexplore.ieee.org/document/8015507/
• Additional Information: Published in: 2007 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), doi:10.1109/FUZZ-IEEE.2017.8015507
• Contract Date: Apr 26, 2017