Extension of the fuzzy integral for general fuzzy set-valued information
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...
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| Format: | Article |
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Institute of Electrical and Electronics Engineers
2014
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| Online Access: | https://eprints.nottingham.ac.uk/37414/ |
| _version_ | 1848795453478404096 |
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| author | Anderson, Derek T. Havens, Timothy C. Wagner, Christian Keller, James M. Anderson, Melissa F. Wescott, Daniel J. |
| author_facet | Anderson, Derek T. Havens, Timothy C. Wagner, Christian Keller, James M. Anderson, Melissa F. Wescott, Daniel J. |
| author_sort | Anderson, Derek T. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:32:20Z |
| format | Article |
| id | nottingham-37414 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:32:20Z |
| publishDate | 2014 |
| publisher | Institute of Electrical and Electronics Engineers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-374142020-05-04T16:57:06Z https://eprints.nottingham.ac.uk/37414/ 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. 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. Institute of Electrical and Electronics Engineers 2014-11-25 Article PeerReviewed Anderson, Derek T., Havens, Timothy C., Wagner, Christian, Keller, James M., Anderson, Melissa F. and Wescott, Daniel J. (2014) Extension of the fuzzy integral for general fuzzy set-valued information. IEEE Transactions on Fuzzy Systems, 22 (6). pp. 1625-1639. ISSN 1941-0034 fuzzy integral non-convex fuzzy set sub-normal fuzzy set discontinuous interval skeletal age-at-death estimation sensor data fusion http://ieeexplore.ieee.org/document/6722924/ doi:10.1109/TFUZZ.2014.2302479 doi:10.1109/TFUZZ.2014.2302479 |
| spellingShingle | fuzzy integral non-convex fuzzy set sub-normal fuzzy set discontinuous interval skeletal age-at-death estimation sensor data fusion Anderson, Derek T. Havens, Timothy C. Wagner, Christian Keller, James M. Anderson, Melissa F. Wescott, Daniel J. Extension of the fuzzy integral for general fuzzy set-valued information |
| title | Extension of the fuzzy integral for general fuzzy set-valued information |
| title_full | Extension of the fuzzy integral for general fuzzy set-valued information |
| title_fullStr | Extension of the fuzzy integral for general fuzzy set-valued information |
| title_full_unstemmed | Extension of the fuzzy integral for general fuzzy set-valued information |
| title_short | Extension of the fuzzy integral for general fuzzy set-valued information |
| title_sort | extension of the fuzzy integral for general fuzzy set-valued information |
| topic | fuzzy integral non-convex fuzzy set sub-normal fuzzy set discontinuous interval skeletal age-at-death estimation sensor data fusion |
| url | https://eprints.nottingham.ac.uk/37414/ https://eprints.nottingham.ac.uk/37414/ https://eprints.nottingham.ac.uk/37414/ |