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 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.

[1]  M. Gorzałczany A method for inference in approximate reasoning based on interval-valued fuzzy sets , 1987 .

[2]  Thomas A. Runkler,et al.  Properties of interval type-2 defuzzification operators , 2015, 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[3]  Jean J. Saade,et al.  Defuzzification techniques for fuzzy controllers , 2000, IEEE Trans. Syst. Man Cybern. Part B.

[4]  T. Runkler,et al.  A set of axioms for defuzzification strategies towards a theory of rational defuzzification operators , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

[5]  Thomas A. Runkler,et al.  Interval type-2 fuzzy decision making , 2017, Int. J. Approx. Reason..

[6]  E. Walker,et al.  Some comments on interval valued fuzzy sets , 1996 .

[7]  Jerry M. Mendel,et al.  Interval type-2 fuzzy logic systems , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[8]  Woei Wan Tan,et al.  Towards an efficient type-reduction method for interval type-2 fuzzy logic systems , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[9]  Jerry M. Mendel,et al.  Centroid of a type-2 fuzzy set , 2001, Inf. Sci..

[10]  E. H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Man Mach. Stud..

[11]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[12]  Reza Langari,et al.  A defuzzification strategy for a fuzzy logic controller employing prohibitive information in command formulation , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[13]  Thomas A. Runkler,et al.  Selection of appropriate defuzzification methods using application specific properties , 1997, IEEE Trans. Fuzzy Syst..

[14]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[15]  Witold Pedrycz,et al.  A survey of defuzzification strategies , 2001, Int. J. Intell. Syst..

[16]  Jerry M. Mendel,et al.  Interval Type-2 Fuzzy Logic Systems Made Simple , 2006, IEEE Transactions on Fuzzy Systems.