On a 50% savings in the computation of the centroid of a symmetrical interval type-2 fuzzy set

  • Authors:

  • Jerry M. Mendel

  • Affiliations:

  • Department of Electrical Engineering, Signal & Image Processing Institute, University of Southern California, 3740 McClintock Avenue EEB 400, Los Angeles, CA

  • Venue:
  • Information Sciences—Informatics and Computer Science: An International Journal
  • Year:
  • 2005

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Abstract

Computing the centroid of a type-2 fuzzy set (T2 FS) is an important operation for such sets. For an interval T2 FS, the centroid can be computed by using two iterative procedures that were developed by Karnik and Mendel [2]. In this paper, we prove that if the footprint of uncertainty for an interval T2 FS is symmetrical about the primary variable y at y = m, then the centroid is also symmetrical about y = m and its defuzzified value equals m. As a consequence of this, computation of the centroid for such a T2 FS is reduced by 50%, and the importance of obtaining a non-symmetrical interval T2 FS prior to defuzzification is demonstrated.