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...

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Main Authors: Runkler, Thomas A., Coupland, Simon, John, Robert, Chen, Chao
Format: Article
Language:English
Published: Springer 2017
Online Access:https://eprints.nottingham.ac.uk/47316/
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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.
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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/