Abstract
This paper presents a new type of clustering algorithm by using tolerance vector.
The tolerance vector is considered from a new viewpoint that the vector shows a correlation between each data and cluster centers
in the proposed algorithm.
First, a new concept of tolerance is introduced into optimization problem.
This optimization problem is based on conventional fuzzy c-means (FCM) by Bezdek.
Second, the optimization problem with the tolerance is solved by using the Karush-Kuhn-Tucker conditions.
Next, a new clustering algorithm is constructed based on the unique and explicit optimal solutions of the optimization problem.
Finally, the effectiveness of the proposed algorithm is verified
through some numerical examples.
