Fuzzy clustering algorithm for fuzzy data based on α-cuts

This paper presents fuzzy clustering algorithm for fuzzy data based on α-cuts. A new suitable definition for distance between two arbitrary fuzzy numbers based on α-cuts is proposed. We then reformulate fuzzy c-means FCM with fuzzy data and fuzzy centers based on α-cuts. The effectiveness of the proposed clustering algorithm is tested for three fuzzy data sets and then it is compared with other methods; the fuzzy c-number FCN algorithm, Hathaway's FCM algorithm and the mixed-type variables FCM MVFCM algorithm.