A new fast fuzzy partitioning algorithm

•A new fast fuzzy partitioning algorithm is proposed.•The algorithm is able to find a fuzzy globally optimal partition.•The algorithm is able to estimate the most appropriate number of clusters.

In this paper, a new fast incremental fuzzy partitioning algorithm able to find either a fuzzy globally optimal partition or a fuzzy locally optimal partition of the set A⊂RnA⊂Rn close to the global one is proposed. This is the main impact of the paper, which could have an important role in applied research. Since fuzzy k  -optimal partitions with k=2,3,⋯,kmaxk=2,3,⋯,kmax clusters are determined successively in the algorithm, it is possible to calculate corresponding validity indices for every obtained partition. The number kmax is defined in such a way that the objective function value of optimal partition with kmax   clusters is relatively very close to the objective function value of optimal partition with (kmax−1) clusters. Before clustering, the data are normalized and afterwards several validity indices are applied to partitions of the normalized data. Very simple relationships between used validity indices on normalized and original data are given as well. Hence, the proposed algorithm is able to find optimal partitions with the most appropriate number of clusters. The algorithm is tested on numerous synthetic data sets and several real data sets from the UCI data repository.