Fuzzy c-means clustering method with the fuzzy distance definition applied on symmetric triangular fuzzy numbers

The conventional fuzzy c-means (FCM) clustering method can be applied on data, where data features are crisp; however, when the features are fuzzy, the conventional FCM cannot be utilized. Recently, some researchers applied FCM on fuzzy numbers when the used metric has a crisp value. Since difference between two fuzzy numbers can be represented by a fuzzy value better than crisp one, in this paper, it is going to extend the FCM method for clustering symmetric triangular fuzzy numbers, where the used metric has a fuzzy value. It will be shown that the proposed fuzzy distance expresses the distance between two fuzzy numbers much better than crisp metrics. Then the proposed method has been applied on simulated and various real data, where it is compared with several new methods. The experimental results show better performance of the proposed method in compare to other ones.