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Interval Type–2 Defuzzification Using Uncertainty Weights

Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 739)

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.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Siemens AG, Corporate TechnologyMunichGermany
  2. 2.Centre for Computational Intelligence, De Montfort UniversityLeicesterUK
  3. 3.Laboratory for Uncertainty in Data and Decision Making (LUCID)University of NottinghamNottinghamUK

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