Partial Defuzzification of Fuzzy Clusters

  • Slavka Bodjanova
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Two methods of partial defuzzification of fuzzy clusters in a fuzzy k-partition are proposed. The first method is based on sharpening of fuzzy clusters with respect to the threshold 1/k. Sharpening is accomplished by application of the generalized operator of contrast intensification of fuzzy sets to k — 1 fuzzy clusters. The second method utilizes the idea of strong sharpening. In this approach the very small membership grades in each fuzzy cluster are reduced to zero. It is explained how these methods can lead to the well known approximation of a fuzzy partition by its crisp maximum membership partition.


Fuzzy Cluster Membership Grade Fuzzy Partition Maximum Membership Fuzzy Objective Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Slavka Bodjanova
    • 1
  1. 1.Department of MathematicsTexas A&M University-KingsvilleKingsvilleUSA

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