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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.

Authors

Derek T. Anderson

Timothy C. Havens

James M. Keller

Melissa F. Anderson

Daniel J. Wescott



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.

Journal Article Type Article
Publication Date Nov 25, 2014
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
APA6 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), https://doi.org/10.1109/TFUZZ.2014.2302479
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
Publisher URL http://ieeexplore.ieee.org/document/6722924/
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
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.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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