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Extension of the Fuzzy Integral for General Fuzzy Set-Valued Information

Anderson, Derek T.; Havens, Timothy C.; Wagner, Christian; Keller, James M.; Anderson, Melissa F.; Wescott, Daniel J.

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Derek T. Anderson

Timothy C. Havens

James M. Keller

Melissa F. Anderson

Daniel J. Wescott


The fuzzy integral (FI) is an extremely flexible aggregation operator. It is used in numerous applications, such as image processing, multicriteria decision making, skeletal age-at-death estimation, and multisource (e.g., feature, algorithm, sensor, and confidence) fusion. To date, a few works have appeared on the topic of generalizing Sugeno's original real-valued integrand and fuzzy measure (FM) for the case of higher order uncertain information (both integrand and measure). For the most part, these extensions are motivated by, and are consistent with, Zadeh's extension principle (EP). Namely, existing extensions focus on fuzzy number (FN), i.e., convex and normal fuzzy set- (FS) valued integrands. Herein, we put forth a new definition, called the generalized FI (gFI), and efficient algorithm for calculation for FS-valued integrands. In addition, we compare the gFI, numerically and theoretically, with our non-EP-based FI extension called the nondirect FI (NDFI). Examples are investigated in the areas of skeletal age-at-death estimation in forensic anthropology and multisource fusion. These applications help demonstrate the need and benefit of the proposed work. In particular, we show there is not one supreme technique. Instead, multiple extensions are of benefit in different contexts and applications.

Journal Article Type Article
Acceptance Date Jan 24, 2014
Online Publication Date Jan 24, 2014
Publication Date 2014-12
Deposit Date Oct 7, 2016
Publicly Available Date Oct 7, 2016
Journal IEEE Transactions on Fuzzy Systems
Print ISSN 1063-6706
Electronic ISSN 1941-0034
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 22
Issue 6
Pages 1625-1639
Keywords fuzzy integral, non-convex fuzzy set, sub-normal fuzzy set, discontinuous interval, skeletal age-at-death estimation, sensor data fusion
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