Enhanced Karnik-Mendel algorithms

  • Authors:

  • Dongrui Wu;Jerry M. Mendel

  • Affiliations:

  • Ming Hsieh Department of Electrical Engineering, Signal and Image Processing Institute, University of Southern California, Los Angeles, CA;Ming Hsieh Department of Electrical Engineering, Signal and Image Processing Institute, University of Southern California, Los Angeles, CA

  • Venue:
  • IEEE Transactions on Fuzzy Systems
  • Year:
  • 2009

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Abstract

The Karnik-Mendel (KM) algorithms are iterative procedures widely used in fuzzy logic theory. They are known to converge monotonically and superexponentially fast; however, several (usually two to six) iterations are still needed before convergence occurs. Methods to reduce their computational cost are proposed in this paper. Extensive simulations show that, on average, the enhanced KM algorithms can save about two iterations, which corresponds to more than a 39% reduction in computation time. An additional (at least) 23% computational cost can be saved if no sorting of the inputs is needed.