Interval Type–2 Defuzzification Using Uncertainty Weights
- 660 Downloads
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.
- 5.Runkler TA, Glesner M (1993) A set of axioms for defuzzification strategies—towards a theory of rational defuzzification operators. In: IEEE international conference on fuzzy systems, San Francisco, pp 1161–1166Google Scholar
- 8.Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8:199–250, 301–357, 9:42–80Google Scholar
- 12.Runkler TA, Coupland S, John R (2015) Properties of interval type–2 defuzzification operators. In: IEEE international conference on fuzzy systems, Istanbul, TurkeyGoogle Scholar
- 14.Nie M, Tan WW (2008) Towards an efficient type–reduction method for interval type–2 fuzzy logic systems. In: IEEE international conference on fuzzy systems, Hong Kong, pp 1425–1432Google Scholar
- 16.Pfluger N, Yen J, Langari R (1992) A defuzzification strategy for a fuzzy logic controller employing prohibitive information in command formulation. In: IEEE international conference on fuzzy systems, San Diego, pp 717–723Google Scholar