Interval Type–2 Defuzzification Using Uncertainty Weights

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

Abstract

© Springer International Publishing AG 2018. 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.

Citation

Runkler, T. A., Coupland, S., John, R., & Chen, C. (2018). Interval Type–2 Defuzzification Using Uncertainty Weights. In S. Mostaghim, A. Nürnberger, & C. Borgelt (Eds.), Frontiers in Computational Intelligence (47-59). Cham: Springer Verlag. https://doi.org/10.1007/978-3-319-67789-7_4

• Acceptance Date: Sep 27, 2017
• Online Publication Date: Sep 27, 2017
• Publication Date: 2018
• Deposit Date: Oct 17, 2017
• Publicly Available Date: Sep 28, 2018
• Publisher: Springer Verlag
• Pages: 47-59
• Series Title: Studies in Computational Intelligence
• Series Number: 739
• Book Title: Frontiers in Computational Intelligence
• Chapter Number: 4
• ISBN: 978-3-319-67788-0
• DOI: https://doi.org/10.1007/978-3-319-67789-7_4
• Public URL: https://nottingham-repository.worktribe.com/output/884710
• Publisher URL: https://link.springer.com/chapter/10.1007%2F978-3-319-67789-7_4
• 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