A fuzzy c-means variant for the generation of fuzzy term sets

  • Authors:

  • T. W. Liao;Aivars K. Celmins;Robert J. Hammell, II

  • Affiliations:

  • Army Research Laboratory, Attn: AMSRL-CI-CT, Building 321, Aberdeen Proving Ground, MD and Department of Industrial and Manufacturing Systems Engineering, Louisiana State University, Baton Rouge, ...;Formerly Intelligent Systems Branch, Army Research Lab, Aberdeen Proving Ground, MD;Formerly Intelligent Systems Branch, Army Research Lab, Aberdeen Proving Ground, MD

  • Venue:
  • Fuzzy Sets and Systems - Theme: Modeling and learning
  • Year:
  • 2003

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Abstract

A fuzzy c-means (FCM) variant is proposed for the generation of fuzzy term sets with ½ overlap. The proposed variant differs from the original mainly in two areas. The first modification ensures that two end terms take the maximum and minimum domain values as their centers. The second modification prevents the generation of non-convex fuzzy terms that often occurs with the original algorithm. The optimal number of terms and the optimal shape of the membership function associated with each term are determined based on the mean squared error criterion. The exponential weight, m, used in the algorithm is found to greatly affect the shape of the membership function. The effect of data size used for the generation of fuzzy terms is also discussed. A generalized π-shaped function with a tunable parameter along with its complement is developed to fit all term sets generated by the FCM variant using various m values.