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Interval type-2 defuzzification using uncertainty weights

Runkler, Thomas A.; Coupland, Simon; John, Robert; Chen, Chao

Authors

Thomas A. Runkler

Simon Coupland

Robert John robert.john@nottingham.ac.uk

Chao Chen chao.chen@nottingham.ac.uk



Abstract

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.

Journal Article Type Article
Journal Studies in Computational Intelligence
Print ISSN 1860-949X
Electronic ISSN 1860-949X
Publisher Humana Press
Peer Reviewed Peer Reviewed
Volume 739
APA6 Citation Runkler, T. A., Coupland, S., John, R., & Chen, C. (in press). Interval type-2 defuzzification using uncertainty weights. Studies in Computational Intelligence, 739, doi:10.1007/978-3-319-67789-7_4
DOI https://doi.org/10.1007/978-3-319-67789-7_4
Publisher URL https://link.springer.com/chapter/10.1007%2F978-3-319-67789-7_4
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information The final publication is available at link.springer.com via http://dx.doi.org/10.1007/978-3-319-67789-7_4

Published as: Runkler T.A., Coupland S., John R., Chen C. (2018) Interval Type–2 Defuzzification Using Uncertainty Weights. In: Mostaghim S., Nürnberger A., Borgelt C. (eds) Frontiers in Computational Intelligence. Studies in Computational Intelligence, vol 739. Springer, Cham

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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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