Fuzzy c -Means for Data with Tolerance Defined as Hyper-Rectangle

The paper presents some new clustering algorithms which are based on fuzzy c-means. The algorithms can treat data with tolerance defined as hyper-rectangle. First, the tolerance is introduced into optimization problems of clustering. This is generalization of calculation errors or missing values. Next, the problems are solved and some algorithms are constructed based on the results. Finally, usefulness of the proposed algorithms are verified through numerical examples.