Interval type-2 defuzzification using uncertainty weights
One of the most popular interval type-2 defuzzification methods is the Karnik-Mendel (KM) algorithm. Nie and Tan (NT) have proposed an approximation of the KM method that converts the interval type-2 membership functions to a single type-1 membership function by averaging the upper and lower members...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer
2017
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| Online Access: | https://eprints.nottingham.ac.uk/47316/ |
| _version_ | 1848797514908565504 |
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| author | Runkler, Thomas A. Coupland, Simon John, Robert Chen, Chao |
| author_facet | Runkler, Thomas A. Coupland, Simon John, Robert Chen, Chao |
| author_sort | Runkler, Thomas A. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | One of the most popular interval type-2 defuzzification methods is the Karnik-Mendel (KM) algorithm. Nie and Tan (NT) have proposed an approximation of the KM method that converts the interval type-2 membership functions to a single type-1 membership function by averaging the upper and lower memberships, and then applies a type-1 centroid defuzzification. In this paper we propose a modification of the NT algorithm which takes into account the uncertainty of the (interval type-2) memberships. We call this method the uncertainty weight (UW) method. Extensive numerical experiments motivated by typical fuzzy controller scenarios compare the KM, NT, and UW methods. The experiments show that (i) in many cases NT can be considered a good approximation of KM with much lower computational complexity, but not for highly unbalanced uncertainties, and (ii) UW yields more reasonable results than KM and NT if more certain decision alternatives should obtain a larger weight than more uncertain alternatives. |
| first_indexed | 2025-11-14T20:05:06Z |
| format | Article |
| id | nottingham-47316 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:05:06Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-473162018-09-27T04:30:25Z https://eprints.nottingham.ac.uk/47316/ Interval type-2 defuzzification using uncertainty weights Runkler, Thomas A. Coupland, Simon John, Robert Chen, Chao One of the most popular interval type-2 defuzzification methods is the Karnik-Mendel (KM) algorithm. Nie and Tan (NT) have proposed an approximation of the KM method that converts the interval type-2 membership functions to a single type-1 membership function by averaging the upper and lower memberships, and then applies a type-1 centroid defuzzification. In this paper we propose a modification of the NT algorithm which takes into account the uncertainty of the (interval type-2) memberships. We call this method the uncertainty weight (UW) method. Extensive numerical experiments motivated by typical fuzzy controller scenarios compare the KM, NT, and UW methods. The experiments show that (i) in many cases NT can be considered a good approximation of KM with much lower computational complexity, but not for highly unbalanced uncertainties, and (ii) UW yields more reasonable results than KM and NT if more certain decision alternatives should obtain a larger weight than more uncertain alternatives. Springer 2017-09-27 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/47316/1/type2defuz_v4.pdf Runkler, Thomas A., Coupland, Simon, John, Robert and Chen, Chao (2017) Interval type-2 defuzzification using uncertainty weights. Studies in Computational Intelligence, 739 . ISSN 1860-949X https://link.springer.com/chapter/10.1007%2F978-3-319-67789-7_4 doi:10.1007/978-3-319-67789-7_4 doi:10.1007/978-3-319-67789-7_4 |
| spellingShingle | Runkler, Thomas A. Coupland, Simon John, Robert Chen, Chao Interval type-2 defuzzification using uncertainty weights |
| title | Interval type-2 defuzzification using uncertainty weights |
| title_full | Interval type-2 defuzzification using uncertainty weights |
| title_fullStr | Interval type-2 defuzzification using uncertainty weights |
| title_full_unstemmed | Interval type-2 defuzzification using uncertainty weights |
| title_short | Interval type-2 defuzzification using uncertainty weights |
| title_sort | interval type-2 defuzzification using uncertainty weights |
| url | https://eprints.nottingham.ac.uk/47316/ https://eprints.nottingham.ac.uk/47316/ https://eprints.nottingham.ac.uk/47316/ |