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Generating an interpretable family of fuzzy partitions from data

Abstract : In this paper, we propose a new method to construct fuzzy partitions from data. The procedure generates a hierarchy including best partitions of all sizes from two to N fuzzy sets. The maximum size N is determined accordingly to the data distribution and corresponds to the finest resolution level. We use an ascending method for which a merging criterion is needed. This criterion is based on the definition of a special metric distance suitable for fuzzy partitioning. The distance we define does not handle the point coordinates, but directly their membership degrees to the fuzzy sets of the partition. This implies the introduction of the notions of internal and external distances. The hierarchical fuzzy partitioning (HFP) is carried independently over each dimension, with the possibility of reintroducing the multidimensional context by considering an output heterogeneity indicator at a fuzzy set level. The generated partitions can be combined in all dimensions. To help choosing, in each dimension, the best suited resolution level, we assign a validity index to each partition within the hierarchy. Due to the merging technique, all the fuzzy sets in the various partitions are interpretable as linguistic labels
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S. Guillaume, B. Charnomordic. Generating an interpretable family of fuzzy partitions from data. IEEE Transactions on Fuzzy Systems, Institute of Electrical and Electronics Engineers, 2004, 12 (3), pp.324-335. ⟨10.1109/TFUZZ.2004.825979⟩. ⟨hal-01318299⟩

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