Analytical solution methods for the fuzzy weighted average

  • Authors:

  • Xinwang Liu;Jerry M. Mendel;Dongrui Wu

  • Affiliations:

  • School of Economics and Management, Southeast University, Nanjing, Jiangsu 210096, China and Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 900 ...;Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089-2564, USA;Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089-2564, USA and Machine Learning LAB, GE Global Research, Niskayuna, NY 12309, USA

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2012

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Abstract

For the fuzzy weighted average (FWA), despite various discrete solution algorithms and their improvements, attempts at analytical solutions are very rare. This paper provides an analytical solution method for the FWA based on the conclusions of the Karnik-Mendel (KM) algorithm. Compared with the two current popular kinds of @a-cut based computational methods for the FWA (mathematical programming transformations and direct iterate computations), our method is precise, and, has a concise structure, efficient computation process, and sound theoretical proofs. We propose two algorithms for computing the analytical solution of the FWA. Two numerical examples illustrate our proposed approach.