Super-exponential convergence of the Karnik-Mendel algorithms for computing the centroid of an interval type-2 fuzzy set
KM algorithms are widely used to perform type-reduction and to compute the centroid of type-2 fuzzy sets. Because KM algorithms are iterative, there has been some concern about their convergance time. Many people have observed, from simulations, that convergence occurs rapidly, i.e. under 10 iterations; but, it is one thing to observe this in simulations and another thing to mathematically prove super-exponential convergence, as is done in this paper. So, by mathematically proving superexponential convergence, Mendel and Liu have provided the type- 2 fuzzy set community with concrete evidence of the speed of the KM Algorithms.
Citation : Mendel, J. M. and Liu, F. (2007) Super-exponential convergence of the Karnik-Mendel algorithms for computing the centroid of an interval type-2 fuzzy set. IEEE Transactions on Fuzzy Systems, 15 (2), pp. 309-320.
ISSN : 1063-6706
Research Group : Centre for Computational Intelligence