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.

Abstract

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.

Citation

Anderson, D. T., Havens, T. C., Wagner, C., Keller, J. M., Anderson, M. F., & Wescott, D. J. (2014). Extension of the Fuzzy Integral for General Fuzzy Set-Valued Information. IEEE Transactions on Fuzzy Systems, 22(6), 1625-1639. https://doi.org/10.1109/TFUZZ.2014.2302479

• 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
• DOI: https://doi.org/10.1109/TFUZZ.2014.2302479
• Keywords: fuzzy integral, non-convex fuzzy set, sub-normal fuzzy set, discontinuous interval, skeletal age-at-death estimation, sensor data fusion
• Public URL: https://nottingham-repository.worktribe.com/output/739261
• Publisher URL: http://ieeexplore.ieee.org/document/6722924/
• Additional Information: © 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.